All major airlines allow dogs, but have specific requirements for bringing a dog on board. The dog must be placed in an airline-approved carrier, which must either fit underneath your feet or be placed in the cargo hold. All dogs that travel on major airlines must have current health papers.
Check with the specific airline that is flying to the destination you want to find specific rules they have on size, breeds, and type of restrains for dogs that may travel. Your dog may only qualify for travel in the cargo area and the current temperature can be a problem.
Most airlines allow dogs in the underbelly of the plane. However, if you want your dog in the cabin you will need to check with the airline first. Most smaller breeds are allowed. If your airline allows it make reservations for your dog to travel. He will need to be current on his shots and have a health certificate.