I would get a temp/humidity gauge where you can put the probes in the incubator but keep the actual unit outside of the incubator, so you don't have to open the incubator to see the readings.

Vibration can be mitigated by putting the incubator cooler on a pillow. If you keep to the interstates the ride should be fairly smooth.

Obviously don't be in a hurry and when stopping for food/pee breaks someone should always be with the vehicle so you don't have to lock it up and potentially have it overheat in the sun.

Also be careful of the temperature of the floor in the vehicle if that's where you want to put the incubator, as the transmission can throw a lot of heat without you realizing it.