Answer:
Dogs are symbols of fidelity, which may be pointing back to this promise that's happening between or this contract that these two people are buying into here, perhaps symbolic of the fidelity or faithfulness in this union or marriage of these two people.
This isn't any ordinary dog. This is actually a very rare breed of dog called an affenpinscher. And it, too, may be suggestive of this family's, the Arnolfini family's, great wealth.
