Remember that your pet is also a member of the family, and deserves some consideration in the moving plans.

Plan for your pet’s trip to the new home.  Most pets will make the move in a car with the rest of the family. In the event that you’re traveling by air, you’ll need to make arrangements for your pet several weeks in advance.

Ideally, on moving day your pet should stay elsewhere, preferably in a familiar place: a favorite kennel service, or at a kind friend or relative’s home. With all the comings and goings at your house – strange people and vehicles, and constantly opening doors – there are just too many chances for your pet to have a meltdown or meet with an accident. If your pet must be in the house, find an empty room with the least commotion and put your pet there. Put a sign on the door to clearly indicate that the room is not to be entered. Ensure your pet has enough fresh water and some familiar toys.
Your pet will be picking up on the family’s signals in the weeks before and after the move. If you’re experiencing stress, your pet will be tuning into the change. No matter how crazy life gets, try to maintain (as closely as possible) your pet’s feeding, watering, play, and exercise routines. Keep their familiar foods, toys and bedding accessible.
Cats are far more territorial than dogs are. Cats need to feel that they are in control of a changing environment, whereas dogs are far more attached to their owner than they are to the actual house. So make sure your cat always has a nook or cranny or box to hide in or under at both ends of the move.

Make sure your pet is wearing identification.  Pets can be unpredictable when their home life is upset. There is a higher risk of your pet escaping in the weeks before and after the move.
When traveling by car with your pet, remember to restrict its food intake several hours ahead of the trip, and during the trip too.  Your dog will be much happier if it has been well exercised before the trip. Be sure that any food you give your pet is easy to digest, and use water from your regular home supply; changing diet or water sources are common causes of diarrhea and vomiting from upset stomachs. If in doubt, check with your veterinarian for food recommendations. Don’t forget extra food for the arrival (can opener too!), medications and vet records, familiar toys, new identification tags, and something with a reassuring scent.