Well....my daughter married a farmer in Tennessee, got married here (in Oregon), and a wedding present from me was about 5 of my best laying hens.
They traveled pulling a small "stock" trailer set up for the chickens. We put in plenty of soft bedding and apple slices to give them some moisture during the trip. They stopped and fed and watered them in the late afternoon.
The hens even managed to lay an egg or two on the way, and arrived in Tennessee just fine (which is most of the way across the continent from me).
Just so you have some perspective, the family smiled and waved as about 70 years earlier, my grandmother (with my father and two siblings in tow), loaded up a couple of Conestoga wagons, a flock of hens in the tail gate of one, and traveled from the dust bowl in South Dakota to a new homestead in Oklahoma. They stopped in late afternoon and let the hens forage. By the way, they got an egg or two on the way.
So yeah, it is very doable. Just make sure they have a stable enclosed trailer, some air flow, plenty of nesting material to soften bumps, some apple slices for moisture during the trip, and food and water at evening. You may even get a few "eggs on the way." LOL.
Good luck with your move.
LofMc
EDITED TO ADD: And yes of course, get a clean bill of health from your Vet for the chickens and check local laws.