Building the pass through from a living area into a garage is most likely a fire code violation. Call your local Fire Marshall *and* your local building code office and ask questions. Be sure and speak with an actual inspector/Fire Marshall, not an office person. Don't trust your contractor to do this for you...sometimes they will tell you something will pass and it won't.

Here is a snippet from the web of general attached garage wall construction requirements:
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Garage Wall Construction

* Following are tips from the IRC and UBC on fire-resistant construction for garage walls:

* The wall separating the garage from the house needs to have 1/2-inch-thick gypsum board on the garage side. The UBC requires the use of Type X gypsum board, as well as fire tape to seal joints on drywall and gypsum board. UL has tested and assigned a one-hour rating to a wall assembly with Type X gypsum board on both sides and fire-taped.

* If there is any habitable space above the garage, 1/2-inch gypsum board is required on the garage ceiling. In addition, all of the supporting walls need to be clad with 1/2-inch gypsum board. The UBC requires a fire-rated floor-to-ceiling assembly.

* The entry into the house from the garage must have a 20-minute-rated fire door�"a minimum 1 3/8-inch thick solid wood or steel door. The UBC additionally requires the door to be self-closing and self-latching.

* There should be no opening for air duct systems in the garage, such as returns or vents. These might actually "fuel" a fire. Any ducts passing through the garage or penetrating its walls or ceilings are required to be a minimum of 26-gauge sheet steel or other material approved by the AHJ.

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That last point especially applies to your plan, which is why I doubt it would pass inspection. Installing a door after all inspections are passed can be done, but personally I wouldn't live in a house with a pet door or other opening leading into the garage, whether it was in the wall or in the door.