Delta Airlines Pet Cargo Policy. Delta Air Lines is a major airline, operated by Delta Air Lines, with headquarters in Atlanta, Georgia. Traveling with your pet can certainly be stressful at times, especially if you are gone for a while. You always want everything to go smoothly and your dog to enjoy its travels as much as possible. With the pet cargo policy of Delta Airlines Pet Cargo Policy, however, you can rest assured that your Dogs and cats will be transported safely and comfortably.