Air carriers have individual rules on the number of pets allowed per flight, age minimums, weight limits and the size of container that can fit under a seat. Generally, if your dog is about the size of a cat, she should be accepted in an airline cabin.
Check with individual airlines before booking to find out if dogs are allowed on flights and if your dog falls within size limits. Many air carriers sell soft-sided, ventilated, leak-proof pet-travel bags that fit under the airplane seats. Airlines require that a pet must be able to stand and turn around comfortably within the carrier. Your dog should be calm and comfortable enough with air travel that you can take her out and carry her through the airport security checkpoint and not take her out for comforting during the flight. The dog's carrier stays under the seat for at least takeoff and landing, and airlines may require it stays stowed for the duration of the flight. Be prepared with water and snacks to give your dog.