I completely disagree with Kate Mc Bride. As a professional agility trainer, I travel every other weekend with my dogs, as do a ton of my friends. Accidents occur, and when they do, uncrated dogs get thrown from the car and usually killed. Not only should your dog be crated when in a car, the crate should be tied down.
Dog seatbelts are an option, if there is not room for a crate. However, not all seat belts are created equal. Champion is considered the best seat belt system, and you can Google it. You're looking for a seat belt with metal attachments, so they will not break in an accident. Be sure to fully understand how to instal and use the seat belt so that your dog is safe.
If I remember right, the Champion harness has been crash tested to 30 mph only. There is a crate that has been extensively crash tested, but it is over $1,000...unfortunately.
This issues has been recently brought to fore in the large National agility community when a very popular, international level handler was in a wreck with her dogs. Only one was crated. Three dogs died. :(
A few more tips. Do not put the dog in the passenger seat with the air bag activated. This can crunch and kill the dog, even in a low mph wreck. Also, if you have an SUV or wagon, keep the dogs out of the back. That is the crumple zone, and if hit from behind, it will collapse like a pop can. The passenger zone is protected and where all human and furred family should ride.
When traveling, the crate is also extremely useful in hotels or family/friend's homes. Being able to know your dog is safe in the strange environment is a real plus. You can Google the DVD "Crate Games" by Susaln Garrett to learn how to make the crate nothing but a big toy to your dog. :)
Have fun on your trip and kudos to you for seeking ways to keep your dog safe on your journey!!! Traveling with well-trained dogs is SO MUCH FUN!!!