It's a good idea to take along a pet carrier for crating your pet. If your dog is sure-footed, this might not seem like much of an issue, but any animal can go flying if you come to a sudden stop. To prevent injury (and to keep accidents contained), consider crating your pet while you're moving down the road. Alternatively, pet stores carry "seat belts" for pets; there should be an appropriate size for your pet. Make sure you know how to use the restraint safely before embarking.
Make sure you have plenty of food and water for your pet. Buy food ahead of time and take along as much as your storage capacity will reasonably allow. Keep it in an airtight container so the food stays fresh. If your pet tends to get carsick and vomits or froths at the mouth, feed him or her after you've done your day's mileage. Some medications can help with carsickness -- ask your vet.
Put down a water bowl with fresh water and see that your pet has access to it whenever you're stationary or camping. At rest stops along the way, always offer your pet fresh water. It goes without saying -- although pet tragedies every day necessitate repeating this -- that you should make sure your pet is never subjected to extreme temperatures, hot or cold. Don't forget that the temperature inside a closed vehicle is often more extreme than the outside temperature. Make sure that your pet has fresh air, and don't leave your pet unattended in an air-conditioned RV; if the power fails, your pet could die.
Your dog feels as cramped as you do after hours of traveling. It's important that you walk him/her when you take rest stops. If your pet is a cat, walks aren't an issue, but plenty of stretching room is. For sleeping and comfort's sake for both cats and dogs, bring along a pet bed if you've got room.
Once you make camp, abide by the camp's pet policies. Request a site away from other campers, shady if it's hot, sunny if it's cold. Be as quiet a neighbor as possible -- nothing ruins a camping experience for others like your constantly barking dog. Adhere to leash laws, for everyone's safety. If there's any risk of your pet's biting, bring a muzzle so there are no mishaps if well-intentioned strangers approach. Check with campground management about dog-walk areas and "poop-scooping" policies. Always clean up after your pet. If you are traveling with a feline friend, think through the cat-box arrangement. Having extra litter, a covered litter box, plastic bags for disposal, scoop, and baking soda to cover the bottom of the box will keep mess and odor to a minimum.
Take along a stake and long leash so your dog can participate in your campground fun, being sure never to leave him or her unattended. Keep water within reach and keep any possible entanglements out of the way. Portable enclosed pens are great for both dogs and cats if you want to allow them to enjoy the outside with you and to keep everyone safe at the same time. Never let your pet wander.
Take a look at the Humane Society of the United States site for its excellent information on traveling with pets.
Do ask yourself before you go, would my pet be happier at home? If your pet is joining in the RV fun, happy trails to you and your four-footed friends.