I've used AC for internal and international flights with the cat, and they're good with animals. Buy yourself something to eat, though... and bring a warm coat.
For the other questions, DEFRA and AC are the people to ask. Maybe the Ministry of Agriculture in Canada. I'm wondering if you'll need another vet check in TO, and whether they'll want an export fee. Hopefully not! Check to see how you pay for the cats flights. I had to pay cash at the counter for Madeira's flight to Japan, AC didn't accept credit cards. I was not prepared.. I thought I had already paid.