Breeding Sun, Moon and Rainbow dragons

Yes, the breeding time is always the same as hatching time for all dragons, rare dragons included. This means you can check your breeding time to know what dragon you're going to get; you're getting a Tree Dragon in this case.

You can verify the hatch/breeding time for any dragon with the Wiki's Dragon Reference Chart to check which kind of dragon you might be expecting. Alternately you can just look in the store in-game. Look for dragons matching some/all of the elements of the Parents (combined) that have the same hatch time as your remaining Breeding time.

Note that the upgraded breeding cave/island reduce your breeding time by 20%, but the incubation time will remain the same.

Ben Brocka's answer is certainly accurate, but I thought I'd do some dragon math for posterity, to share some of what I've learned about the game. Below is guidance to make coins as fast as possible (which can in turn fund treats for dragon leveling and decorations and other purchases for XP). If your goals are achievments, unique dragon collecting, park beauty, etc then of course take this guidance with a grain of salt. The spreadsheet I compiled to crunch all of this is epic in proportion, so if you've got some other nuanced question you want to know the answer to.. by all means ask.

Fire Habitats Good - Earth Habitats Bad

Up through level 8, Small Fire habitats with 2 Flower Dragons are the most economical provided you check your park around 4 times a day (which you'll be wanting to do to breed, hatch, and feed). At level 8 you unlock the even more attractive Large Fire habitat, which becomes the best habitat (full with Flower Dragons) if you are checking your park more than twice a day. For below math I assumed checks are spaced evenly throughout the day, and dragon are level 6 (see more on that below).

Before level 8:

^{** considered disadvantaged due to breeding time and risk of breeding Tree Dragon (28 hrs lost)}

At level 8:

At level 11-12 some options open up to you, and it becomes more about how you want to play the game. You can focus on some easily acquired dragons to start building a cash reserve, or instead start chasing the rares.

Some options to consider:

^{** Beat by a thin margin, but the best overall dragon/habitat combo above 3 checks/day through level 30.}

Above level 12 the only really noteworthy unlock is the Large Metal Habitat. Once unlocked, and fully outfited with Magnetic Dragons it is the best non-rare 1 check per day habitat, at 115,200 / day.

Dragons and Leveling

• As implied above, your first priority for spending should be hitting your habitat max for each level, and upgrading those habitats when possible.
• Your second priority should be filling habitats with dragons. With the Fire habitats this is easy since you can buy Fire dragons and they incubate quickly. When transitioning to Cold habitats you can breed a Fire Dragon with a Lichen Dragon, which will produce Flower Dragons for your Fire Habitats and Lichen and (if you're lucky) Blue Fire Dragons for your Cold Habitats.
• Adding dragons creates income faster than leveling individual dragons, but leveling dragons also provides a valuable income increase, especially once the dragons/habitat cap is hit. Treats/dragon-level are the same for all dragons, and the amount doubles for each level. With active large treat farms it is generally possible to upgrade dragons to level 5-6 as fast as you can produce them. These upgrades should be spread evenly across all dragons to maximize earning potential. Upgrades above level 6 climb steeply and should be more targeted towards the dragons with highest earning potential.

Breeding for Cash

The DragonVale Wiki has a great link on this here: http://dragonvale.wikia.com/wiki/Breeding_for_Profit

Assuming you keep your breeding cave fairly busy in the early levels, this becomes a more significant potential for revenue at higher levels. Consider:

• Breeding and selling 2 Water Dragons / day (8 hours breed+incubate) = 500,000 /day
• Breeding and selling 4 Air Dragons / day (4 hours breed+incubate) = 1,000,000 /day

Both of which are relatively easy to come by once you've unlocked them and have the cash for the eggs and habitat. If you really want to farm, some metal dragon hybrids have an even higher payout later (see the link).

Breeding Opportunity Cost

Breeding is one of the main bottlenecks of the entire game, especially early on (unless you are buying trunks of gems with your real monies). As such, think twice about breeding mating pairs that have a potential for long cycle times. This is especially true of any earth combination, because even after such a long wait, what you get in return is typically not awe inspiring.