1. Invest in a good carrier. If your rabbit cage fits in your vehicle, your rabbit can travel this way, but most cages take up too much room. Some people use carriers meant for dogs and cats, although it can be awkward to get your rabbit in an out of a front-opening carrier. You may want to invest in a rabbit travel carrier, which usually are top and front opening and easier to manage. Make sure you get one big enough for your rabbit. Allow your rabbit to get used to the carrier, first by allowing your rabbit to explore the carrier on its own (just put it on the floor during playtime, and put a few favorite treats inside). After a while, put your rabbit in the carrier for a few minutes at a time, with a favorite treat or toy.
2. Prepare your rabbit for the ride with some practice runs. Start out with short trips in the car, and work up to longer (30 minutes - one hour) trips. This will help get your rabbit used to both the carrier and the sensation of riding in a moving vehicle. Your rabbit may already be used to short drives (to the vet, etc.), but it is still a good idea to take a few longer drives to get your rabbit used to longer trips. If at all possible, use a seatbelt to secure the carrier.
3. Plan ahead. Pack extra food (same as the rabbit normally eats), water from home and a water bottle that can attach to the carrier, and some favorite treats. Get a health certificate from your vet, and consier getting your rabbit microchipped in case he or she gets away on you. If you need to make stops along the way, find hotels ahead of time that will let your rabbit stay too. Also pack some cleaning supplies like paper towels and vinegar for any messes or spills. Place a blanket or cardboard over the seats in the vehicle where the carrier will sit to protect from any stress-induced urine spraying.
4. Be prepared. Place some pellets and hay in the carrier. You may elect to not leave the water bottle on the carrier at all times as it will probably leak with movement. However, offer the water bottle regularly (e.g. for a few minutes every hour), ideally during rest stops. If your bunny prefers, you can offer water in a dish during stops. Also when you stop, offer your bunny his or her favorite treats to encourage eating, as many rabbits don't eat much due to the stress of traveling. You may want to place a puppy training pad on the bottom of the carrier for extra absorbency.
5. Prevent overheating. Rabbits do not tolerate temperatures over about 70 F very well. Do not allow the carrier to sit in direct sunlight in the vehicle. Never leave your rabbit unattended in the vehicle on a sunny day, as the inside of a vehicle can overheat rapidly in the sun, and when you do make short stops be sure to park in the shade and vent the windows. Use the air conditioning in the vehicle if you have it, but do not alow the vents to blow directly onto the rabbit's carrier. If you do not have air conditioning, place a damp towel over the carrier, and place an ice pack wrapped in a small towel in the carrier. Also make sure no heat vents blow directly onto the carrier, even on cool days.
6. Plan for Overnight Stops. If your trip is longer than a single day, pack a puppy exercise pen to use as temporary overnight housing. Also pack a piece of cardboard or linoleum and some newspapers or heavy towels to line the pen and protect the floor from accidents and chewing. Don't forget a litterbox and litter, and make sure you have enough supplies (food, water from home, and cleaning supplies) to last the duration of your trip.
7. Prevent Escapes. Your rabbit should only be taken out of the carrier in enclosed spaces to prevent escapes. A stressed rabbit may dash away if it gets out of the carrier outdoors.
A successful vehicle trip with rabbits depends on planning ahead and planning well, and preventing as much stress as possible.