We travel with Bailey every year down to NC (from MO, an 18 hour trip) and she's pretty good. We have a crate, but Her Majesty prefers the door open so she can come and go as she pleases. (We do shut her in the crate whenever we stop for gas and to switch drivers - about every two hours.) We bought a deep plastic pan that fits on the floor behind the front seats and use those absorbent crystals (had to get her used to those before the trip since it's not something we use at home on a regular basis.) The high sides help contain any 'accidents' if Bailey misjudges the size of the box.
Unless your cat is used to going outside in unfamiliar territory (we did have one cat, Brando, who was quite happy walking along with the dogs, no matter where we were), I'd leave her in the car. Less stress for her and you don't have to worry about losing her if she slips out of the leash.
Whenever you take a break at a rest stop or gas station, let her out and offer her some water (I doubt she'll eat, although you can try.)
Once you get to her new home, it would probably be less stressful for her if you put her in a room by herself to acclimate (maybe with some of your boyfriend's clothes) for a little while. She'll let you know when she's feeling brave enough to explore the rest of the house...
This is Bailey. (The Queen Is Not Amused...)