Airlines are generally very efficient at handling live animals in transit.
Speak with the airline that you intend to fly with, so that they can tell
you the necessary requirements.
There is no live animal inspection at the airports, but when flying aboard,
you must be prepared to deal with the health regulations of the country into
which you are traveling.
In the US, interstate travel by common carrier requires a written health
certificate from a veterinarian.
Advice relative to taking your dog interstate or into another country is
available from your veterinarian, or from travel agents specializing in dog-related
trips.