I still can't really imagine the two of them having a pet (probably for the same reason I have a hard time imagining them having children together). I actually see them having children together more easily than I do having a pet. But then again I feel about pet!fic the way some feel about daddy!Brian fic. But that is just me. I feel there is more basis in canon for children than pets. There is one reference, Wolfram Ethan's cat, in five seasons of Qaf. There are several references to children or babies throughout the entire series. Not that I am a daddy!Brian or Daddy!Justin fan, just see more basis of it. But as far as crack fic is concerned. Let's bring on the parakeets or the love birds, or gerbils or.....iguanas, it's all good.
OR, Justin has been in New York for a while, is living on his own, and gets a cat as a sign of independence and wanting something warm to sleep with in the absence of Brian. Interesting thought. This one I actually can see.
But the problem with pets is that the two of them are already high maintenance on their own, so they'd have to have a really chill pet for Brian not to freak out about it. exactly:-)