We recently travelled from Brazil to Canada with our dog and my husband only had his visitor visa at the time.
Make sure you follow the guidelines of EACH airline that you will be flying. We ended up flying on 3 different airlines, so we had to abide by the rules of each one.
The biggest problem for us was how to carry the dog - we have a small dog that had to go in the cabin with us. They MUST be in a SOFT sided carrier.
Make sure you get the rabies shot and have proof of that with you. Also, make sure each airline provides you with proof that you have paid etc to abide by their rules.
We had no problems at customs. They almost didn't notice the dog. She said "Ok.. nothing to declare.. you may go." And I said, "Actually, I circled that we have a dog".
It was very quick, didn't ask for any documents (even tho we had all sorts). Just make sure you have EVERYTHING in case they do ask for documents.
Good luck!