Your pet can travel on the plane with you (either in-cabin, as accompanied baggage, or as cargo). Your pet will be charged accordingly. Some airlines no longer offer this option and some countries do not allow pets to enter the country in-cabin.
How can I travel to another country with my pet?
Most countries require pets to arrive with a health certificate (also called an international health certificate, a veterinary health certificate, a veterinary certificate, or an export certificate). You must verify the country requirements each time you plan to travel with your pet.