There has to be a fire separation between the living space and a garage. The passage door between the house and the garage has to be a "rated" door. It might be a 1-3/8" solid core door that is "rated", or a 1-3/8" metal clad door, or a 20-minute fire rated door.
A passage door from the garage to the exterior does not have to be fire rated. It SHOULD be exterior rated, and are usually metal, but does not have to be fire rated.
Keep in mind that a dog door allows easy access for someone to enter your house.