How can you get a pet on dofus

As far as simply buying Pets goes then you can either buy them from other players, merchants or the Pet Markets in Bonta and Brakmar.

Well, I'm not a paying member, I can't go out of Incarnam, so can I only buy them from merchants and other players?

You can buy any pet you want but you may not equip the oet if you are a free player, unfortunate news.