exiting with a dog back to country of origin

For your return to Canada, let Dr. Islas do your paperwork. He will know exactly what you will need at that particular time. Things change regularly.

The thing to remember is that the airlines require more than the countries do. They don't want to be in a position where an animal is refused entry once they have arrived, they are responsible. So, if you have what the airline wants, you are fine!