Yes, don't forget her water and bowl
I also travel with a first aid kit (benadryl, syringe, bandages, aveeno oatmeal wash in case of allergic reactions, ear medicine, etc.) just in case. Also shampoo and brushes (you never know what they might get into).
Don't forget her favorite toys and blanket for the car. Have a wonderful trip and I'm sure she will love anything you do for her special birthday