As we look back at the many themes of zombie fiction, one of the prevailing images we see over and over again is the survival of a man and his dog. There is a relationship that forms between Man and His Best Friend that is different from the bond between man and any other thing. A dog is eternally loyal, always protective and will love you unconditionally. As a matter of fact, they make excellent companions for a family or person on their own in the Zombie Apocalypse. Assuming the disease is a human born strain that a dog can't catch, it will be the best protector you could imagine. In the case that animals can become infected you probably want to stay as far away from dogs as possible. They chew things.
That said, not just any dog will do. You do not want to burden yourself with a small dog, slightly bigger than a rat. It will be more than useless and may slow you down at a time you need to move quickly. Ideally, we are looking for a breed that has traditionally been used as guard dogs. I find that Doberman Pinschers and German Shepherds best exemplify the qualities we are looking for. These two breeds, though they have scary reputations, are two of the most loving, loyal, dedicated and protective breeds around. Because they have been bred for loyalty and protection they tend to adopt the people they are with. They treat you as a member of their family and protect you as such. And these dogs are fully capable of protecting you.
Treat your dog right and it will not only take care of you, but it will take care of your family. They will let you know when zombies are approaching. They will protect you if they deem something a threat. They will love you and your family or group.