If our dogs don't go, we don't go. We consider our two as part of the family and they like camping. Fireman is right about the restraints. Ask my wife. She ended up with our 58 pounder on her lap. Worse yet is when she bothered me while driving. I bought restraint harnesses for both of them and use heavy nylon ropes with eye splices to attach them to the child seat restraint system in the back seat. They have sufficient freedom to move around in back and only enough to allow the nose to reach just over the front seat back cushion. I may find that is still too long and I can adjust it if need be. It is for the dog's and your safety.
Our dogs sleep in the trailer. It is best to take your dog if you go somewhere. Sometimes ours will stay in the trailer if it is too hot out and we are outside but usually they are within a few feet of us and certainly in sight. Also depending where you go, wildlife could pose a danger as well if the dog is left out unattended.
Take a five gallon jug of water from home. Give them only water from the jug. As you use water from the jug, keep it full by adding the local water. Repeat the process when you leave for home. Dogs digestive systems are as sensitive to changes as yours. This give them time to get used to the change in water slowly.
Feed them lightly before you leave and provide water as needed. They can get car sick too. Get them used to it with short trips. If your dog travels often and is fine with it, these precautions are probably not necessary. Dry dog food is best as it is easiest to store and doesn't spoil if left in a bowl all day. Don't forget that the dog needs a regular pit stop too.
Give your pooch a chance to get used to the trailer before you leave. This represents a significant change in the environment. At the beginning of each camping season, we put them in the trailer for short periods of time while we pack so they get to know this is home too. This keeps the anxiety level to a minimum.
Make sure you dog is vaccinated against rabies, is on heartworm preventative and is vaccinated for Lyme Disease if you are in tick territory which is just about everywhere.
Microchip your dog. My dogs are registered with a microchip company that has a website that you can put info on it like when and where you are on vacation, numbers to call, etc. Put identification with a phone number of a person back home that can be called in the event your dog is lost. I often will put my campsite number on the girls.
Carry a doggy first aid kit. See
http://www.superk9.com/articles/health8.asp
As stated, please clean up after your dog. People will love you for it and probably want to kill you if you don't.
One could write a book on this. Check your local pet store for books on travelling with your dog. There is good info at a number of websites as well. Try
http://www.petsmart.com/pet_library/home_remedies/travel.shtml