My thoughts are in the middle ground on this. Since you're in a trailer, it's pretty well protected from outside elements (cold nights, animals, etc) so that's good. I agree with other posters that an adult will fare MUCH better with this setup than a young dragon would because of the reasons provided. You may want to wait until your dragon has grown (a year or so) or consider adopting a docile, healthy adult dragon who is being re-homed near you.
It also comes down to their individual personality too. Some dragons may be terrified and stressed out by the moves as Kingofnobbys mentioned. That can be a real threat to their health and happiness. Some dragons on the other hand seem to enjoy a bit of adventure and would be fine with it. I've had my dragons on long car trips and their reaction has been mostly curiosity to most of the things they encountered and I felt it was a positive experience for them offering some enrichment instead of keeping them in a tank all day. That's just from my limited experience and I realize it could go very differently depending on the dragon.
Before going all out I suggest trying some short car rides around town and see how they handle it. Offer time in the yard and see how they handle it. If you have a dragon who doesn't seem to enjoy that then it's a no go. Otherwise I'd ease into trying the camping a bit.
Even with an adult you'll need to take precautions. They need to stay very close to you when outside and preferably be on a leash/harness. This will help prevent them from running off (which can be instinctual and not being able to in some cases could be stressful) and can provide protection from predators (hawks, eagles, etc).
I have a collapsable baby play pen for travel that I use and it works pretty well. Providing time outside can provide adequate UVB but you'll still want a basking lamp for inside. A halogen flood light and adjustable stand will do the trick - just set it to provide the 100-110 basking range in part of the pen during the day. It's good to provide some hides as well. You will also need to carry cleaning supplies (vinegar/water, F10SC, paper towels, rags) to clean up after them and also a supply of food (veges for adults, younger dragons or for an extended stay you'll need bugs - black soldier fly larvae work well for travel). So you don't really travel lightly with them and that's another thing to keep in mind.
I may be missing some things to consider, but that's the general idea. I'm not against doing this but I advise careful consideration of the points everyone is mentioning before doing so and you'll want to ease into it and be well prepared, that's all.