Whether your trip is long in duration or distance, these ideas will help you to be sure you have everything you need for your dog.
Find out if there are any viruses or diseases that a more common problem for the areas you will be travelling too.
For example: when I was travelling east from the west coast of Canada I found out that heart worm was a high risk problem there and that a dog should be on heart worm medication. This could be a possibily anywhere in the world or something different may exist. So be sure to check this before leaving home as it will save you a huge hassle on the road. Veterinaries are commonly very busy and it can be difficult to get an out of town appointment on short notice and you will have to pay for a full first time client visit plus medication. If your regular vet has seen your pet recently they are more likely to be able to sell the medications without an appointment since they will know your pet's history. Another possible option on the road is to phone your local vet have them fax a prescription authorizing medication without an appointment. You will have to talk to your vet per case, I'm not sure this would work with everything.
2. The Food You Buy at Home For Your Dog is NOT Garunteed On the Road
If you require certain food for your pet you will either need to calculate enough food for your entire trip (plus extra as your dog likely to require more food as a camping road trip is likely to bring on more activities than normal). Or you can phone ahead/check online for the pet stores in the cities you will be going through to see what brands they carry to know if you will be able get food you like on the way.
When I went on my first long distance trip from Canada down to Arizona I made the mistake of thinking everywhere would carry dog food that I like for Riley. I feed Riley dehydrated raw food on trips... it does not exist everywhere!! So be aware for any special diet your dog is on.
After that experience.. before I left on our cross Canada trip I did phone stores on the east coast to see if they carried our brands. So I knew which cities I would be able to stock up in. Calling ahead can save you a TON of time driving too so you don't end up running around randomly to multiple stores.
3. Your Dog Won't Have Regular Access to Water
Chances are a water bowl isn't going to stay in place while you are driving.... so you have to remember to get in the habit of always offering them water when you make stops since they won't be able to self regulate like when you are at home. They are relying on you for water!
4. Tick Remover Makes a Great Keychain
You never know when you are going to find a tick...and it suuuuuucksss when you find one in the middle of a walk and don't have a way to remove it. Not what you want to be thinking about for the next hour! I think keys are the thing you're most likely to always have close to you on a trip so you can have quick access to get them off of your pet. The sooner they are removed the better the chance of avoiding disease transmission. I find the little plastic hooks with a slit work really well. Just follow the directions on the package.
5. Battery Powered Mini Fan
I'm pretty sure this suggestion is going to find its way in to many posts. It has been huuuuge huge help to Riley on trips. Make sure to get one that comes on a big clip so you can clamp it to anything in front of where your dog is laying. For Riley he will usually put his head down, stop panting and relax within a few seconds to a minute. It makes me feel so much better to see him be able to stop panting on hot days! I find a charged up set of batteries will go an entire night on low. And then you can recharge them the next day when you are driving in a usb charger that plugs in to the cigarette lighter. Keep a couple of sets so that you can rotate and always have the fan ready to use day or night.
6. Pet First Aid Kit/Emergency Carrying Harness
It's a good idea to have a kit handy to clean any wounds that arise, tweezers for shrapnel, wraps to keep sores protected etc. There are many kits available to get you the basics you need. The second item is a harness that I will be able to hoist Riley in to, to carry him out on my back should he become injured on a hike. Have a plan for getting your pet out of the forest.
7. Nice Surface
If you are going to be spending a lot of time hanging out in the outdoors, where your dog is likely to be laying down for long periods. A cozy place that they can call theirs will be very comforting for them. It will also be nice on their bodies to not be on cold and hard ground surface for long periods of time regularly. It's nice if they can have an option if they wish to do that or not. I have dog sized inflated mattress for Riley now. Granted he doesn't always choose it, but he often does, so I know he appreciates the choice!