Maybe this is an unpopular opinion, but, although I'm really sorry for the loss of your dog, that's something that many people go through, and we can't just all have our lost pets added to the game, as much as we would like that to happen. Our family went through it recently too, but as much as I would like to see it, I can't, and won't, expect the developers of Party Animals to specifically add our pet to the game as a consolation for our personal feelings over recent loss.
Not to mention, I highly doubt that a caricatured version of your pet, molded to the same basic shape as every other playable character in the game for hit-box reasons, would ever do your dog justice.
Nor would seeing your best friend being smacked in the face by a shovel. Sorry, but I don't think this is the way.