How do I get a pet related to one of the nations?

Like fire benders get a dragon when you first join and so on. I need a otter bear and a fox for the quest but all I ever see in the different areas are around three to four different egg types and nothing else.

You can't just find a starter pet. You can only get the other three through the Black Market or the Trading Post. Foxes are available through a certain quest, which you also need to use the Black Market for.