This time of year?
Drive, without question.
See America first (but check ahead for "pet friendly" motels). Five days in each other's company will be an experience that you and the dog will both remember. This will all be new and strange to her, and her insecurity will be greatly lessened by having you within "touching" distance. In your case, she'll not be with you forever, and you'll have gained immeasurably by having experienced and being able to later recall just how close the bond between dog and man can be.
Years ago, I drove my daughter's furniture and dog from Texas to Ohio in Midwinter in a rental truck, about 1200 miles. The dog, a mixed breed Ridgeback/Terrier cross about 6 at the time had been abandoned in national forest and rescued by her when she was just starting A&M, and had never spent much time with at our house.
After 2 1/2 days together (she riding on a quilt on the floor between the two bucket seats of the truck, mostly sitting up with her head on my thigh)), 2 motel nights, and some rest stops in the first snow she had ever seen, she developed no little affection for me. For the rest of her life, another decade, even after a couple of years of separation, every time in which she or I entered a room or house where the other was, she ran to me, simply to put her head on my leg.
Dogs remember, and our memories of their remembering form the stuff of remembrance.