Unless you have some kind of attachable restraint system back there, this is a terribly bad idea. Not only for the poor dog, who will be hurled forward in a frontal impact, but for you. If she weighs about 45lbs, keep in mind that Force = Mass x Acceleration. At a mere 20 mph actual impact velocity, that is 900lbs of force potentially aimed at someone's head, depending on the vector. If not for her life, perhaps for yours or an occupants, please reconsider. Back
seat with a dog harness is the solution...for shedding, install a full width
seat cover. They work well.