I saw a survival film once and the expert on there said it's a human thing. Over 99% (not 100%) would not eat their pets.
BUUUUT, that figure dropped to 15% when asked would they eat their neighbors pet. Believe me when you are truly hungry you'll eat anything.
Go hunting for food? Lol. In truth dogs don't work on zombie apocalypse because there are no food(zombie animals, zombie dogs).
Dogs don't work when there are no animals around. That is why Herbivores are more important at start. Unless the dog goes cannibalism.