Summarize the following:
While carrying a dog on a stretcher or driving them, wedge anything you have that's soft around the dog's body to keep their body from moving around unnecessarily.  Pillows or rolled up towels and blankets are ideal. Unless it is quite warm, use a blanket, towel, or piece of clothing to wrap the dog during transportation.  Not only will this calm the dog down, if will prevent heat loss that may occur due to shock or injury. If anyone else is around, have someone else drive to the vet. This will allow you to help keep the dog from moving around. Further, this will keep you from driving distractedly. Call the veterinary hospital to let them know you're on your way. Describe the dog's injuries to help the vet prepare for your arrival and start helping the dog as efficiently as possible. If no one else is around to drive, complete the call before getting on the road. Another benefit of calling ahead is ensuring that the vet you're heading for is capable of treating your dog. If they are not, you may be able to have a vet meet you there for emergency service, or they can tell you where to go instead.
Minimize spine and neck movement during transportation. Cover the dog. Have someone else drive. Call the vet en route.