Does Southwest Airlines Have a Pet Policy Yes, the airline allows vaccinated domestic cats and dogs to fly in the cabin with their owners.Each person may only bring one pet carrier, and all pets must be in authorized under-seat carriers. Each pet container is subject to a non-refundable cost from the airline. Pets are not permitted on overseas flights or in the cargo hold. Service animals are allowed as long as they adhere to certain rules. Southwest's pet-friendly policies guarantee both travelers and their pets a relaxing and secure travel experience.