Travelling with a pet in flight will not trouble you any more. I have travelled 2 times with my dog to Canada.
I will suggest you Air Canada they serve the best services and comfortable seats.
You need to submit some documents. There are some rules and regulations to follow like:
1. Properly carried in soft ventilated bags in the prescribed size.
2. The pet must be properly muzzled and leashed and the weight of the pet including the container should not exceed five kgs. Pet will be carried at an additional charge and will not be included in the free baggage allowance.
3. Valid health and rabies vaccination certificates.
4. Entry permits and other documents required by countries of entry or transit
5. Pet accepted at owner's risk.
6. The owner will be responsible for compliance with all governmental customs and health requirements, including quarantine arrangements at destinations.
7. The owner will assume all the risks of injury, sickness or death of the pet accepted for carriage.
8. A declaration indemnifying the airline will be obtained from the passenger.
9. The owner must ensure their pets meet the quarantine requirements. Pets may be subjected to quarantine at the destination at the owner's expense.
10. A trained dog or a service dog to assist blind or deaf passengers will be carried free of charge in addition to the normal free baggage allowance.
11. Maximum 2 animals- pets or service dog are permitted per aircraft, with the concurrence of the commander.
For more rules refer to
https://reservationsnumber.org/air-canada/and solve your problems immediately.