cat carriers are good for adult dragons for short drives (2-5 hours). For babies I suggest a small cardboard box with old towels or claen rags for padding. Wrap a cloth around a heat pack if needed but if the car temps and outside temp are not likely to drop below 65F or reach above 90F then they won't need additional heating or cooling. IN a dark box they will just sleep or rest. Don't feed before you leave for the trip but make sure they have the opportunity to drink something. Once you are at your new place, set up their tanks then put the dragons in and let them bask and settle for an hour or two before feeding. (if not enough time to feed before lights out, then skip feeding altogether). Feed normally the next morning.
If your dragons are at least 3 months old, they can do fine with one day without food. If much younger, it would be best to plan to drive first thing in the morning and get them settled into their cages as soon as you can after arriving then feed after an hour to settle and bask. Another note, if it's sunny, don't leave the dragons in the car or don't park the car directly in the sun as it will heat up very fast and overheat your dragons.
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PHLdyPayne