It doesn't matter in Gladiator that Romans didn't use dogs on the battlefield, or that the dog disappears from the movie immediately afterward. It's a very simple equation: The good guys are whichever team the dog shows allegiance to, because the dog would never make that kind of mistake, especially if it's an adorable dog.
You can see it in Hellboy, where we're introduced to the giant, demonic, bad-tempered hero as he picks up and hugs a kitten. In fact, at one point, Hellboy actually causes an almost-certainly-fatal multi-car pile-up in order to save some kittens, and that only makes us root for him harder. In Equilibrium, the exact point at which Christian Bale turns from cold, merciless murderbot into sympathetic hero is the moment he rescues a small puppy, and the audience happily forgets that he'd earlier allowed his wife to burn to death. Clint Eastwood's classification as the "good" in The Good the Bad and the Ugly seems to come almost entirely from a 10 second scene in which he pets a tiny kitten that's sitting adorably in his hat.
"Tell me where Tuco is and then get off my ranch."
Note, however, that this rule only applies to some animals. Dogs and kittens almost always work, but fully-grown cats can be ambivalent. A tiny monkey dressed in a Nazi uniform probably won't do the trick either.