Maybe a Maltese
They're covered with long silky white fur (not fur under hair like many breeds) and they do not shed at all. They don't get much bigger than 7 or 8 pounds as adults. They were bread to be companion dogs and are excellent with children and even infants. They socialize well with other dogs and even cats too. All around a stable, loving, small and clean breed of dog that's just about perfect for children.
You can read more here:
http://en.wikipedia.org/wiki/Maltese_(dog)