Phoenix Hatchling This pet drops off of Kael'thas Sunstrider, the final boss in the BC Heroic Magisters' Terrace. It has an 11% drop rate from him, it also has a 0.2% chance to drop from the reward bag given to tanks/healers occasionally from the LFG tool (source wowhead.com). If you do runs for the White Hawkstrider mount (dropped by same boss) often then you'll likely run into a couple of these little guys along the way.
This little pet lends a considerable edge to combat when you're leveling him up with other pets. The three moves he learns first are
Burn,
Cauterize, and
Immolation.
A very good strategy I used while leveling him was to put him as the first pet in my line up and immediately cast
Immolation as your first move. Then you can switch it out with another pet that is a more tanky sort (I used my Onyxian Whelpling) and burn the enemy down while the Immolation continues to burn them adding to the damage even while your Phoenix Hatchling is on the back lines.
The heal that your hatchling has,
Cauterize, also helps tremendously if you choose to play it on the front lines, healing a set amount plus half the damage of the last hit you took. When playing him at the front while leveling it is still a good idea to set up Immolation first before whittling away at their health with Burn and maintaining your health with Cauterize.
When you have leveled it up to 20 and get your final move,
Conflagrate, then your little hatchling is powerful enough to take out weaker pets (especially mechanical pets) with as little as two hits. By using a combination of your abilities first hitting them with
Immolate and then
Conflagrate, you dish out a crazy amount of damage!
The first move you have the option of keeping
Burn or switching to
Peck, this doesn't make much of a difference as they both deal the same amount of damage. If you need flying damage for utility then taking Peck would probably be a good idea, I had a flying pet - Pterrordax Hatchling - in my line up so I didn't have need for it and kept my phoenix as pure elemental damage.
It is a good idea to experiment with your timing of abilities with pets that can cause weather effects too. As an example I took my Onyxian Whelplings ability
Scourched Earth and set it up then switched my Phoenix back out since it ignores the damaging effect. With this I was able to take Conflagerate and have the burning bonus with it and still keep my heal ability Cauterize because I didn't need to have Immolate to apply that burning status.
Have fun with it, and good luck! :3