I personally really like the idea of raising your pet. I know it is not a new idea but Blizzard have done something similar (Falcosaur mounts) in the past. But they never really transfer that into pet oriented classes. And why not?
I really don't mind doing a series of quests to find a baby 'battle' pet sitting next to its slain mom, battle and win its trust and raising it into an uniquely majestic hunter pet through series of..idk...more quests. It'll be nice if we can have a pet that hunters can 'upgrade' throughout the expansion like we did with the legendaries.
Same concept can be applied to other classes such as warlock pets, priest and pally avatars or maybe even shaman wolves.