If you hit a bump, swerve to avoid an obstacle, or brake suddenly, your dog could easily fly out of the truck. If the fall doesn't injure or kill the dog, it is likely that another car will. And in an attempt to avoid hitting the fallen dog, another driver may cause ensuing accidents. Tying the dog to the truck bed is dangerous. Ropes and leashes become nooses if the dog should be jolted out of the truck.
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. 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.