Wind is a painful hazard. Wind whipping through the dog's ears is full of dirt, debris, and gravel that can lodge in the eyes, nose, or ears and cause serious damage.
The Law in Oregon
Oregon Revised Statute 811.200 prohibits carrying a dog on an external part of a vehicle unless the dog is protected by framework, carrier, or other devise to keep the dog from falling from the vehicle. This offense is considered a Class D traffic violation.
Take your dog along for the ride, but let her ride secured in the front with you. She will enjoy the trip a lot more if she doesn't have to fight for her life against gravity, momentum, and traffic to get there. Use a humane tether, a secured crate, or place a canopy over the bed.