With proper care, you can ship cats and dogs easily and safely. Dogs and cats will do quite well being shipped from one place to another. However, the transit process is unfamiliar and disorienting to the pet, so many owners prefer to use the method that keeps the pet in transit for the shortest time. Often, this means flying in a sturdy carrier in the baggage compartment of a plane.
This compartment is climate-controlled and pressurized, the same as the cabin, so the pet is not subjected to extremes of temperature.
Some air carriers allow small pets to ride with their owners as carry-on luggage in the passenger compartment, provided they are small enough to move around in a kennel the same size as a carry-on suitcase.