Zootopia pets, what are they?

So, only mammals have evolved in Zootopia, leaving reptiles, fish, birds and bugs all feral. But I imagine pets would still be a thing. But would there be lizard parks? Certain animals people would eat, and others they wouldn't? For example, we have horses. Could they even ride ostriches and lizards? Have a cowboy culture? Have bird parks? Walk penguins? Have illegal pet fights? It just feels as though "animals" must exist in some way.