It's just a level spell gain, not required by a quest.
The pets are split into 3 classes, much like adventrers:
Earth = Fighter/Tank with low DPS but high agro. Good for soloing tough mobs.
Aery = Scout/DPS, medium armor. Good for soloing normal to heroic mobs.
Fire = Mage/DPS, weak armor but high DPS. Good for normal mobs or when in a group.
Fire is my favorite due to it's wild attack. I root the mob at a distance and pet-attack. Fire pet lands a high damage nuke, takes 4 steps toward the mob, lands another high damage nuke, takes another 4 steps toward the mob, repeats all the way in to melee range.
With me landing additional damage, the mob is usually dead before the Fire pet get to it.
Scout/Aery pet has been the most versitile for soloing normal to heroic mobs. It's medium survivability and you casting additional damage kills the mob quickly with few pet-heals.
Earth pet is used when you need to take down a ^^ or greater mob. It's good armor and HP will make it last a long time and take a beating...like any good tank wants to.
Once you get your last pre-level-50 pet of a series, (i.e. level 38 Earth pet is the last Earth pet you get), spend whatever money you have to make them Adept III. You will pay a crazy amount of money, but consider that the pet is your main weapon, and worth it.
Additional offensive or defensive pet stances will make your pet better. Learn how a Off/Def stance will affect different pets. For example, I use the Fire pet with a Defensive stance to increase it's survivabillity, and add a pet-proc buff (Blazing Presence) to increase it's damage.
Good Luck!