Name of Peter Pan Dog

I was talking with my wife the other day about whether or not Peter Pan had a dog. I know that there was a dog in the children's house but in "Never, Never Land" I don't remember there being any dogs. Fairies there were plenty of but dogs, no, I don't remember a single one. Well I guess it could be argued that Peter Pan had plenty of imaginary pets so he didn't really need a live dog. Anyway Tinkerbell might have gotten insanely jealous if she had found Peter Pan spending too much time with a pet dog.