If your dog or cat meets the requirements listed in Southwest Airlines pet policy to travel in-cabin, you will need an approved airline pet carrier. The maximum size carrier that can be carried on a Southwest flight is 8.5 high x 18.5 long x 13.5 wide.If you are traveling with a soft-sided carrier, the height should be measured when compressed. There must be sufficient room for your pet to stand up and turn around in the carrier.he maximum size carrier that can be carried on a Southwest flight is 8.5 high x 18.5 long x 13.5 wide. If you are traveling with a soft-sided carrier, the height should be measured when compressed. There must be sufficient room for your pet to stand up and turn around in the carrier.