Dogs tend to adapt to moving more easily than cats. If you travel by plane, a small dog may be able to fit under your seat in his pet carrier. Consult with your vet before the move in order to take the necessary measures to reduce stress. And make sure your flight is a direct one so that your dog's carrier won't be exposed to the elements while he waits for a plane transfer. Call ahead to find a hotel that accepts pets so as to avoid leaving your pet in the car overnight.
Birds present a unique scenario for any mover.
Most states require a health certificate for birds, and some states require that birds have a series of health tests performed prior to entry in their new home states. Again, check with your vet long before your move takes place, and have him or her perform all necessary tests and sign all paperwork ahead of time. Doing your homework will avoid the possibility of any snags upon your arrival at your destination. If you plan to transport your bird by car, remember that birds don't respond well to temperature changes. Maintain a comfortable temperature in your car at all times.