The service you choose also affects the Southwest Pet Fee for your pet, which in turn affects the cost of your pet's ticket. You must be able to provide proof of your pet's vaccinations and medical history in order for them to travel with you. You can make reservations on our website. Pets must be transported in crates, bags, or carriers that can fit under the seats of your car. You are allowed to bring your pet's carrier into the cabin if it meets these requirements.