The bonus proficiency is a domain feature. Domains are a class feature. The multiclassing rules state that you gain the class features when you get a new level in the new class. It then lists exceptions to this with channel divinity, extra attack, spell casting and unarmored defense. Domains are not listed, so it seems that the bonus proficiency is the more specific rule and you gain the domain proficienices.

You could use a breastplate, and should use a heavy shield, but anything more than that costs you too much: you really aren’t that squishy, and you can expect things to get better on their own in a few levels anyway. Sinking more resources into it isn’t worthwhile.

All 2nd-level characters are pretty squishy.

Your AC is fairly low,¹ but 16 HP isn’t at all bad for a 2nd-level character.² For comparison, the absolute best you’re likely to see at this level is a Barbarian 2 with 27 HP.³ He had to put a lot of investment in to get that, though, and has to be in the thick of things, and does not have access to any kind of healing. You have built-in healing and (most likely) great saves, and your goal is to be hanging back anyway.

So really, you aren’t that squishy. Definitely not so squishy as to justify something drastic like dipping fighter or setting a feat on fire. You are squishy in the sense that all 2nd-level characters are, but in a level or so that will be largely mitigated.

Avoid expensive options for improving AC or HP

Taking levels in other classes or using feats are very, very expensive ways to do anything. Because your squishiness is very much a temporary problem, you want to avoid sinking resources that are particularly precious into this.

Spellcasters multiclass poorly

As a spellcaster, you do not want to fall behind on your spellcasting. Spells are the most powerful force in the game, you want to get higher-level spells ASAP. Fighter, on the other hand, is a very poor class, and is not remotely worth waiting another level for the next level of spells.

Armor Proficiency isn’t worth a feat

Full-plate armor is quite expensive at your level, has significant drawbacks in terms of armor check penalty and weight, and provides “just” +5 additional armor AC over a chain shirt. Now, +5 is a fair bit, but armor AC is of only marginal value: a lot of things just outright ignore it.

Meanwhile, feats are one of the scarcest and most valuable resources in the game. You get very few of them, and some of the things you can do with them are very powerful. That +5 armor AC is probably worth the various drawbacks that full-plate has... but only probably, not even close to being so worth it that it’s also worth burning a feat on it.

You can definitely work with what you have

Mundane items are fairly cheap, and this is what they are for. That’s where you improve your squishiness.

The primary options are, unsurprisingly, armor and a shield.

You can wear up to medium armor: medium armor, though, does kind of suck

Personally, I really dislike the medium armors. A breastplate would give you +2 armor AC over a chain shirt, but costs more, weighs a lot more, has significantly higher armor check penalty, and reduces your movement speed. If +5 is only kind of OK, you can imagine how I feel about +2. Even though you don’t need a feat for it, I wouldn’t actually get a breastplate. A (masterwork) chain shirt remains my recommendation.

If you really care absolutely not at all about any skills that take an armor check penalty, though, a breastplate can work. It does slow you down though, and you really don’t want that.

Playing with a crossbow does hurt you though: you want a shield

A crossbow requires two hands to use properly. That makes it difficult to use a shield, and shields are very good things for buffing clerics. Yes, without a crossbow you’re probably stuck doing nothing while the allies you’ve buffed finish off the opposition, but that’s a temporary situation; in a few levels, you’ll have a lot more spell slots to play with.

As you yourself say, you’re doing very little damage with your crossbow. Worse, that’s probably not going to improve much as you level up: if you think you’re doing very little damage at 2nd level, at 8th level that same damage is going to be truly pointless. Giving up a shield for this is not a good idea. If you had good Strength and Constitution, clerics can make excellent melee characters, and those clerics should use a two-handed weapon of some sort, but if you’re doing support/buffing, a shield is very-nearly-free AC, plus it’s a second platform to put magic properties on.

So ditch the crossbow, and use a shield. If you want to maintain your ability to take pot-shots, you can use javelins or some other one-handed thrown weapon. It’s not really necessary, but it can’t really hurt, either.

As for which shield, there is almost no reason for you to not use a heavy shield, but if for some reason you want that hand available, a buckler is nearly as good. You probably will never use a shield bash anyway, so it’s really just a question of an extra AC vs. having a hand free.

Positioning and tactics are crucial for everyone at these levels.

You are supporting and buffing; that means stay out of combat, keep tougher characters between you and ranged threats, and take cover when you can.

A mount can help, temporarily

Buying a warhorse is an option; they’re not very expensive, and they do provide a lot of mobility. They are also unaffected by your armor, which means you can much more easily use a breastplate if you like.

On the other hand, you have to make Concentration checks to cast spells if your mount moves the same turn you cast a spell, and that’s rough (DC 10 + spell level, when you only add +4 to the check, is a problem). You also don’t have Ride in-class, which means you only have a +2 on the check: enough to be pretty confident in your ability to move from place to place, but not to do anything fancy (even guiding it without using your hands requires a DC 5 check, which you have a 10% chance of failing).

Additionally, as a Medium human, you have to ride a Large mount – and there may easily be dungeons that won’t accomodate one, which will be very annoying.

The real problem with mounts, though, is that most of the typical ones are pretty low level. Fine for now, but don’t expect a warhorse to make it to 11th level. Even if you took Mounted Combat (which greatly improves a mount’s AC once per round), sooner or later someone will dedicate the time to get past that – and Mounted Combat, as a feat, is pretty expensive. Either way, by mid levels most attacks are pretty likely to kill a typical mount in one hit. Using a mount past the early levels tends to require that you get one as a class feature (e.g. animal companion, paladin special mount, etc.)

To add insult to injury, the recent FAQ on mounts makes them almost unusable when they’re not a class feature. No running or charging, for example. As a support/buff cleric, you may not have problems with this, but you very well might.

In the long run, your spells have got you covered

Clerics are one of the top-5 most powerful classes in Pathfinder, almost-purely on the basis of their spellcasting. Your class’s survivability is on the very high end. At very-low levels, spells are a little more difficult to use. In a very few levels, however, it will become easy to buff yourself very well.

Thus, anything you do to improve your survivability now, is probably a bad idea if you could have used that same thing to improve your spellcasting. You don’t want to multiclass, because that’s a level you could have used to improve spellcasting. You don’t want to use a feat for armor, since there are plenty of feats that make your spellcasting better.

You do have a much bigger problem

Far more significant than any “squishiness” you have noticed, is the fact that your Wisdom is quite low for a cleric. Wisdom 16 is a typical low-end value for a cleric. Wisdom 14 is very limiting, drastically reducing your access to bonus spell slots and making the saving throws against your spells extremely easy to beat.

Meanwhile, the Charisma 18 just doesn’t offer that much to you: healing in Pathfinder is weak, and that includes Channel Energy. Until you get the heal spell, healing is pretty much out-of-combat-only, barring emergencies. And out of combat, a cheap wand of cure light wounds will allow you to top off your party without touching your spell slots, and is standard adventuring gear (your party should be willing to pool funds for one; by the time you finish it, 750 gp for another should be chump change).

So generally, a cleric would prefer to have your Charisma and Wisdom swapped (or Constitution 14, Wisdom 18, and Charisma 12, honestly). Someone with Charisma 18 is usually better off in another class, that will put that Charisma to better use (read: base spells on it). It’s well beyond the scope of this question, but it may be a question you want to ask separately.

1. ^{A typical 2nd-level cleric would wear a chain shirt or breastplate, and use a heavy shield, for 16-19 AC depending on Dex and armor choice.}

2. ^{Your Constitution, on the other hand, is a little low. For preference, I’d put Constitution as second-most-important stat for a support/buff cleric, which in practice probably means 14. Losing 1 HP per level does hurt you, but it’s not critical.}

3. ^{Base 18 Constitution, +2 Con from race, maximized d12 at 1st, high-average 7 roll from 2nd. Would go up to 31 HP during the 2 rounds of Rage each day.}