My daughter transported 5 chickens in the back of a trailer set up as a mini-coop from Oregon to Tennessee.
They all made it just fine. The RIR's still laid during the journey. She let them out for foraging a bit each stop (I think they had a portable pen) as it took them a number of days to reach their destination.
You've only got 6 hours, a relatively short distance. Just make sure they are stable for transport, being able to settle nicely on the floor.
Dog crates work well for this type of short distances. If you have, or want to purchase, the kind with the top opening door is really nice for birds (versus the front opener for dog or cat entrance).
It helps to cut up apple slices to place in the crate so that they can have some nutrition and fluids during transit. You should only need to offer feed/water at the beginning before loading and then at the end after unloading. If it is a really hot day, obviously offer some water at a rest stop.
But for the short 6 hour trip, cages/crates will work well. If your portable coop is stable enough, you may be able to place the crates on the floor of the coop for transport, depending upon its size. If they look like they can travel stable in that, as it is smaller (like the mini-trailer) they might travel well in that coop, but if they have too much room to move they can hurt themselves in transit if they startle....so cages or smaller confined areas are best.
LofMc