What fascinates me is that it's a portrait of an individual dog rather than what we might expect (just look at the expression around the mouth and eyes). We might have expected something a little more collective, abstract and symbolic, an expectation evident in the archeologists' guesses that the dog was attached to a temple for healing.
The expression is so cute like a happy dog greeting its human. But then I was thinking it looked like the other pup of the She-wolf, who suckled Romulus and Remus, hoping to get some milk when they were done.