Had a beautiful Grey African parrot and he was stolen along with some TVs, computers and other things. I don't really care about the electronics just the bird.
Some Tenant's policies do cover animals (several of my insurers do), however the perils they cover them for may be limited or there may be a limit per animal or per loss. You would need to speak with your broker as NO ONE here can see your policy and tell you for sure.
No, animals aren't covered, sorry.