United Airlines loves animals of all kinds. They accept small cats, dogs and birds in the cabin; rabbits, hamsters and guinea pigs as checked baggage and other animals including parrots, cockatiels and ferrets, in United Cargo. (Shipping by cargo is for items, like some pets, that you cannot check as baggage. Your pet may or may not be on the aircraft with you). If you have a short-nosed dog, check your date of flight, as some breeds and mixes are not allowed in cargo or as checked baggage from June 1 through September 30 of each year.