Okay, so I haven't tried running an incubator from a car inverter (cigarette lighter adapter) but I have tried running other electrical devices such as fans (for my dogs in crates in the back) and crock pots (for parties). I have found there is a definite limit to the amount of watts/amps whatever those inverters can handle. If you go over, it will pop the fuse and quit working. So, for example, I can run my small crockpot while I'm driving, but not my medium or large one.
I suggest you take your incubator out and try it with your car running for a good while to make sure it can handle the load. Make sure you get through a couple of cycles where the warming element and the fan are both on, as that should be the greatest load.
I would also probably line the egg carton with some bubble wrap, as the road vibration might be bad for the developing chicks.
Taylorhens- I was thinking that it would suck all the energy from the truck and break us down
If this does work I will buy foam or bubblewrap and make sure they are very secure. The only good thing about this is if any of the peachicks do hatch they will hatch at a waterfowl foundation cause thats where we will be staying