Based on the stats given, it appears to me that your best option is to not multiclass.
The most obvious option would be a dip into Monk, to get Unarmored Defense's Wis-to-AC bonus, but that would be trading leather's +1 for your Wisdom's +1. The other abilities wouldn't really add anything to what you already have.
Another option is Barbarian's Unarmored Defense. That would add +2 AC from your Con instead of your Leather armor, but simply changing to Studded Leather (also light, and giving full dex bonus) would achieve the same result. The Barbarian's Rage does add a moderately useful ability, but comes at the expense of delaying your progressing in Fighter/Monster Hunter.
Finally, a 2 level dip into ranger would allow you to pick a second fighting style, specifically "Defense" which grants +1 AC while wearing armor. Again, the Ranger's abilities do not synergize particularly with your other abilities, and delaying your main class abilities for 2 more levels is unlikely to be worth +1 AC.
Also note that none of these options combine. Unarmored Defense is specifically called out under multiclassing as an ability you can only get from a single class, and even the greatest Cheeselords still have trouble finding a way to be unarmored and wear armor at the same time.
It seems like you already have the best option figured out: take the Dual Wielder feat for the bonus AC, and indirect damage increase of 2 one-handed weapons.
While you're shopping for a second rapier, upgrade to a suit of studded leather. This and Dual Wielder will bring you up to 17 AC.
After that, just stick with fighter. At 7th level you can start using 2 superiority dice on damage, as well as automatically maxing superiority dice damage against certain types of enemies. At 10th level, your superiority dice get bigger by a step, becoming d10's.
These options will do more for you than you can get from any quick dips into other classes.
For a build like yours, and for most builds in 5e, multiclassing is a great way to increase the breadth of your skills and abilities, but usually does not add a lot to the depth of them.
As Ethan has pointed out in the comments, don't forget to turn to your teammates for assistance and buffs, as well as doing the same for them where you can.
No, this doesn't work in melee.
At least not the important second half.
- Yes, they can duck behind the corner and hide. All they need to do to be allowed to hide is break line of sight.
No, they can't just pop back out and sneak attack. To sneak attack, they need advantage, and to get that from being unseen they have to still be unseen when they attack (PHB, p. 195):
When a creature can't see you, you have advantage on attack rolls against it.
Unfortunately for the rogue, as soon as they pop out in front of an attacker that's already aware of their presence, they are immediately seen and no longer count as unseen when they attack (PHB, p. 177):
In combat, most creatures stay alert for signs of danger all around, so if you come out of hiding and approach a creature, it usually sees you.
Sneak attack only works if they sneak up on an enemy who doesn't know they're there. Popping out of hiding isn't sneaky, unless the enemy is surprised — and they can't surprise an enemy that is “aware of danger”. When they duck behind a corner in combat, the enemy is aware of danger and watching all around, and is impossible to sneak up on (without unusual circumstances), because that enemy is the opposite of surprised — they are actively on guard.
Does it work at range?
Not easily. It can work as long as they avoid being spotted, but not being spotted is the hard part: since the attacker's location is automatically given away and after that it's easy to see them, special precautions are required to prevent being seen despite the target knowing exactly where they are.
To do that at range you're working with the same rules — they need to be unseen, they need to stay unseen until after they make the attack, and the target needs to fail to locate them after being attacked. It's that last part that makes this difficult — by an explicit rule, attacking reveals a character's location (PHB, p. 195):
If you are hidden—both unseen and unheard—when you make an attack, you give away your location when the attack hits or misses.
So to make this work at range, they need to arrange fictional circumstances somehow to defeat that. The usual way to do this with ranged attacks is to
- attack while unseen (usually in cover1), revealing their location,
- either have attacked while in cover, or move to break line of sight or into cover,
- hide now that they're somewhere that allows a Stealth check,
- move to a new location without that movement being seen, to make their location unknown again,
- then, attack from their new location, unseen.
This convoluted process is often necessary because, at step (1) the ranged attacker has already revealed their location, and all it takes is a successful Perception check to see them (assuming the attacker is not blindingly obvious once the enemy knows where to look) for the advantage from being unseen to be removed. Steps (2)–(5) establish a new location that has not already been revealed, allowing the next attack to be made unseen.
(However, this process can be largely skipped if the hiding spot is so good that Perception checks to see the attacker are likely to fail. To be a good sniper, make a good sniper nest! And hope you're not seen, and have an escape route planned.)
But popping out from hiding in a single location before attacking? No, that won't grant advantage, because just like in the melee situation, the attacker is immediately seen once they move out from their hiding spot to line up the next shot.
Ugh, this is too hard!
Well then, do it the simple way: an enemy that has an ally of the rogue's adjacent to it can also be Sneak Attacked. That allows Sneak Attack every round with no need to fiddle with movement or hiding or seen/unseen variables. Just flank and shiv.
1. This post uses “cover” in the dictionary word's tactical sense, to describe the activity happening in the game fiction. Whether that cover is mechanically represented with Obscurement (PHB, p. 183) or Cover (p. 196) will depend on the exact circumstances as adjudicated by the DM on the scene, as is appropriate.
For Druid + Rogue at level 1; combat is not necessarily required.
Focusing on the rogue's DPR is, IMO, you as DM viewing this party through a very narrow lens. I suggest that, since (1) you only have two players, and (2) neither of them is from a warrior archetype, the adventures that you run for them until they get to second level should focus more on role play, exploration, and evasion / mobility and a bit less on melee combat. But when they do opt for melee combat, they need to try and engage on their own terms. (Credit: Sun Tzu's theory)
In-world, in a narrative sense, the odds that a Rogue and a Druid go and mix it up in the dark halls of a dungeon underground aren't very high. And, by crafting the adventures as suggested you get them working as a team from the get go.
Beyond that, they may not need a tank to create advantage.
How can the Druid help the Rogue get advantage?
Occasionally, with the Help action, but does the Druid player buy into that? Maybe and maybe not, but in any case that is between the two players to figure out. They need to work as a team because there are only two of them.
In some situations, Help will be a good use of an action, in others it will not. Let them figure that out by playing and by making decisions / choices.
Some Druid spells can offer advantage. Again, it is your players who need to work as a team to make the most of this.
Entangle (SRD p. 140)
Note that a creature that fails their save is
From Appendix A, conditions, Restrained
Rogue attack with advantage enables sneak attack.
Faerie Fire (SRD p. 141)
Rogue has advantage, Sneak attack.
From your comment:
It is OK to coach your players if they are new; you are the DM, coaching is a part of your role.
Change your DM'ing paradigm to fit your two-player party
Their first level of adventuring needs to empasize using their wits, not brawn, to accomplish their goals. Between the Druid's spells and the Rogue's ability to succeed on ability checks, and to Stealth around, and to occasionally apply a Sneak Attack if someone gets up into the Druid's grill, you can have some exciting and challenging adventures without a tank.
At level 2 Rogue gets cunning action, Druid gets wild shape; their options expand significantly.
Two of us played a two-rogue party for a session (urban setting) to help a DM get used to running a game. We used ranged attacks, movement, and anything but melee combat to achieve our aims. It's doable, it's fun, and it's still dangerous to the PC.