I'm not sure what the "or bird" part is here for. Birds are animals, seems kinda redundant...
I always desire petting fancy mice.
I guess since you put the bird part, I want to pet a chick. Chicks are just adorable.
....Also, Rowlet.
Well I love pups but you really need to have a lot of time to get a dog for your pets especially when you are a student and your parents don't agree to get you one, so besides it I would love to have a turtle and it seems my mom won't mind me having one.
Birds are classified as Animals too though. Well, I would love to pet an Eagle (Preferably a Golden one as it is also my favorite Animal in general). I have always admired their Grace and feeling of Freedom they inspire !!!!