Does Southwest Airlines Have a Pet Policy vaccinated domestic cats and dogs to travel with their owners in the cabin .Pets must be in an approved carrier that fits under the seat, and each passenger can bring only one pet carrier. The airline charges a non-refundable fee per pet carrier. Pets are not allowed to travel in the cargo hold or on international flights. Service animals are permitted, following specific guidelines. Southwest’s pet policy ensures a comfortable and safe journey for pets and passengers alike.