Right, I'll explain it differently. Every character in Smash Bros. has a copyrighted image. Mario, Link, Samus. Villager is property of EAD, Olimar is property of EAD, Kirby and the crew are HAL's babies, the Pokemon are all under the care of the Pokemon Company and the third-parties are all copyrighted by their respective companies. The image of a dog is not an all-star, isn't a trademark of Nintendo, doesn't legally belong to Nintendo and for that matter is public domain.
It may be a Nintendog by name, but it's a normal dog by nature. Nintendo hasn't made a public domain image playable yet, and I can't see them doing so in Smash 4 (or in any Smash for that matter). Smash Bros. is for Nintendo All-Stars, not real-life, public-domain animals.