It may sound weird, but a smaller carrier is best. One that the rabbit just has room to turn around in. When scared, rabbits feel more secure in a small, enclosed space. If you have watched your rabbit a lot, I am sure you have seen it hunker down in a corner or a crevice when it felt scared, trying to be as small and crammed into the corner as possible. It also prevents injury because if your rabbit does freak out, it does not have enough room to jump around and possibly break its back. For this reason, I recommend a wire carrier, even if your rabbit does not live in a wire cage. The wire provides grip for the feet whereas a cat carrier type one does not provide much, if anny grip. The plastic surface of the bottom, even if it has newpaper, shavings, or other litter in it, will still be slippery. This alone can make the rabbit feel unsafe when it is in a moving vehicle. If you do have to use a plastic carrier, put some cloth in as bedding instead of litter. This at least gives the rabbit something to hold onto, though it will still scoot around a bit with the motions of the car.
is an American company, but it does show a picture so you can see the type of carrier that I am talking about. If your rabbit has sore feet and cannot be on straight wire you can either put some cloth down or get a resting mat and place it snuggly in the bottom of the carrier. Because the wire will grip the cloth or the mat better than plastic, your rabbit will not skid around nearly as much.
Also make sure there is some hay in there for him to eat if he feels like it. Before and after the trip you can brew up some chamomile tea and give it to him to drink. It helps with stress. For liquid during the trip, I usually suggest soaking an apple or a carrot in water overnight and giving him that instead of a water bottle or a water dish. The water dish or bottle will splash and leak due to the motion of the car, and it can get your rabbit all wet, uncomfortable, and more stressed. So the soaked apple or carrot is a good alternative. You can also stop about halfway and offer him some water in a dish or a bottle, then take it away once he is done drinking.