If a character can turn/is turned into a dog or is a talking dog then the character will either age like a human instead of like a dog.
Most writers who have characters who spend a lot of time in the form of an animal, will still have that character age like they were a human. Someone with the power to turn into a particular animal will often retain attributes of his human body in his animal form including age so that a young human will turn into a young animal. The actual rate of aging is most often either ignore or stated to be specifically that of a normal human. Animal companions are companions for life and not just the normal lifespan of their species, but the life of the human.