All placental mammals develop inside their mother. Just like human babies, an umbilical cord connects the puppy or kitten embryo to the placenta and nutrients and oxygen are exchanged between the embryo and the mother.
The puppy or kitten's belly button is located where the umbilical chord was before birth. So, yes they do have belly buttons. It's just a little difficult to spot theirs because it is usually small and often hidden beneath their fur.
|Photo: Puppy Tube|