I took Beardie from NJ to TX by plane, so he had to cope with the bare minimum. The whole trip for him was about 16 hours. I had a small pet carrier with a hand towel on the bottom for traction, and that was all I could pack for him. There are specialized pet moving services, but you'd have to check the cost. Beardie was delivered to and from the airports by a professional pet mover.
The stress can be harder on the dragons than the actual trip! Get some goodies when you get where you're going to tempt them, but mine didn't eat for 2 weeks. The herp vet I took him to said to let him bask in the Sun for a while, so I suppose that helped.
Be sure not to feed your dragons the day before the move, but give them plenty to drink! It can be hard (and stressful), but if my dragon could make it through three airports, I think that yours can do all right on a car ride with you right by them.