Maybe a goldfish or a kitten. Kittens can be declawed (although I would definitely not recommend it) so they will not scratch your child. They are loving, adorable, and can still be played with like a puppy, but aren't a threat. Maybe you could give the child a puppy when it's older. ~Kay
A kitten, they are less work for you because they poop inside. You can get them declawed, which is a good idea, because kittens claws are very sharp. Also, they are smaller than most dogs and they don't bark.