The Walking Dead borrows heavily from the (mass outbreak) zombie genre. In very few other movies or stories have animals ever been able to become zombified. Though they may come up with their own particular explanation for why this is so, I contend that they have it so only because no other stories have ever done it.
And the reasons for that are interesting. Zombies that are truly undead (that is, there is no biological or scientific explanation for them) have had their original souls depart the body and something far more sinister animates them, though it has not returned life to the corpse. I have always gotten the impression that they were hinting that this happens because something defiled the body, either while it was still alive, or after it had died. (And being gored by another zombie likely defiles your body too, thus the infectious nature of it.) Animals cannot be defiled, as their bodies aren't sacred in the way that human bodies are.
But that doesn't satisfy the modern audience, I do not think. Hence Walking Dead's use of a pathogen detectible with medical imaging (as seen in the season one finale). If that explains zombification, then it's not much of a stretch to imagine that the pathogen has no zoonotic tendencies (in layman's speech, it can't be transmitted between species). Of course, this just raises other questions and mysteries, if that happens to be the case.
Note: I don't read comics, and this is based only off of the AMC television show. Several storyline differences have arisen so far, and this could be one of them.