Aang wouldn't give his kids names like Enormous Monster. Imagine Loki naming Appa and Momo. They'd probably have names like Loki's Awesome Bison and The Lemur From The Southern Air Temple. At that point, I think Katara and/or Sokka would insist on taking over naming pets for him.

And instead of going on a quest, Loki would infiltrate the Fire Nation and become Fire Lord. Although if he did go on a quest, I tend to think he'd do a lot of the same things Aang does-- go on sidequests, fly a lot, spend too long on Kyoshi and befriend everyone (possibly not that last one). Aang, on the other hand... I don't think he'd stand for binding his wolf son.