How To Move With Pets by RealtorMag.Realtor.org

Update your pet’s tag with your new address.Make sure your pet’s collar is sturdy and correctly sized. The tag should also include your mobile number and e-mail address so that you can be reached during the move.
Request veterinary records.Ask your current vet to send your pet’s medical history directly to the new vet. Have their contact information handy in case of emergency or if the new vet has questions.
Keep a week’s worth of food and medication with you.You may want to ask for an extra prescription refill before you move. Take the same precaution with special therapeutic foods.
Seclude them from chaos.Keep your pet in a safe, quiet room on moving day with a clear sign posted on the door. There are many light, collapsible travel crates available, but ensure it is well ventilated and sturdy enough for stress-chewers. Also, introduce your pet to the crate before the trip.
Prepare a pet first aid kit.Include your vet's phone number, gauze to wrap wounds or to muzzle your pet, adhesive tape for use on bandages, nonstick bandages, towels, cotton swabs, antibiotic ointment (without pain relief medication), and 3% hydrogen peroxide.
Play it safe in the car.Use a crate or carrier in the car, securing it with a seat belt. Never leave your pet in the bed of a truck, the storage area of a moving van, or alone in a parked vehicle. If you’re staying overnight, find pet-friendly lodging beforehand and have kitty litter or plastic bags on hand.
Get ready for takeoff.When traveling by air, check with the airline about pet requirements or restrictions and whether you must purchase a special airline crate that fits under the seat in front of you.
Prep your new home.Set up one room with everything your pet will need: food, water, medications, bed, litter box, scratch post, and toys. Keep windows and doors closed when your pet is unsupervised, and beware of small spaces where nervous pets may hide. If your old home is nearby, give the new home owners or neighbors your phone number and a photo of your pet, in case your pet tries to return.
Learn about local health concerns and laws in your new area.If you’re moving to a new country, contact the Agriculture Department or embassy of the country to obtain specific information on special documents, quarantine, or costs related to bringing your pet into the country.