Oh, one more thing! You'll want to speak with Ganaar at the Exodar. He'll be able to teach you the last bits of knowledge necessary to care for your pet and train it.
You can find him in the southwest corner of the Traders' Tier.
Knowing how to feed and revive your pet from death is not just an extra "tidbit" as your last teacher so mildly put it. Even more so, training allows your pet to improve in ways they couldn't have on their own.
I've already learned much from the furbolgs, so pay attention and I'll pass the knowledge on to you.