They sure do! Just like you cats, dogs, horses, and giraffes are all placental mammals. Placental mammals develop inside their mother. Nutrients, oxygen, and wastes are exchanged between the developing embryo and the mother through a placenta. An umbilical cord connects the embryo to the placenta. The navel or belly button is where the umbilical cord was attatched to the young placental mammal. So even though you may not notice it unless you look very carefully, dogs and cats do, indeed, have belly buttons.
    Did you know the time it takes placental mammals to develop inside their mother varies? It takes about 20 days for a hamster to develop and about 20 months for an elephant to develop!