TWD is cool in that it took the common, stereotypical, zombie outbreak and changed it just enough to be unique. It is the only 'zombie-verse' where everyone turns, bitten or not, and as far as i know, is the only one where animals dont turn. There have been others where they didnt show turned animals, but TWD is the only one i know of that says outright its just people.
Personally id bring my dog, not sure how long he'd last. he is a solid guard dog and i could see him coming in handy like you said as a detector, but that could also be very bad, drawing more to us. As long as he could figure out to stay out of arms reach of the undead he might stand a chance. My cat id throw in my get away vehicle as well but i dont think he'd have the brains to stick with me and the family, hed probably get lost along the way, but at least i tried..
But in the end the main reason id bring them both is to eat them if it got that bad survival wise.