the placenta is what gives us our belly button, other mammals do have a belly button, just not as obvious as ours, maybe just a little scar, they also have hair that may cover it, but only mammals have this. primates have a similar belly button to us though, because we are so similar
monkey have belly buttons but its the sam elogic as why do soem mammals have a tail but we dont O.o well men do if ya know what i mean but you get my point
You should look between the hind legs.
Art pic of a puppy with an umbilical cord here:
I haven't noticed any on my dogs in the past but I will inspect the next dog I see haha
They do have belly buttons. They're just tiny and covered with fur.