A dog that doesn't weigh more than 20 pounds should be able to fit comfortably enough in a pet carrier that will fit underneath the plane seat.
The pet carrier that the dog rides in must be able to fit under the seat of the plane and the dog must fit comfortably in that carrier.
The size of the space under the plane seat is around 17 inches in depth, 10.5 inches in height and 20 inches in width.
So if you can get a carrier that will fit a bit smaller than those dimensions and the dog can fit into the carrier then the dog should be able to fly on the plane as long as the dog weighs 20 pounds or less.