We moved from NC to CA with 4 kids, the youngest was 6 mos, then 3, 6 and 12. I won't lie, it was hard. We also camped in a tent.
We stopped at every state sign we could and got out and took pictures.
We played every dvd you could get from Cracker Barrel that was appropriate.
We stopped at the fun places; the Badlands, Mt Rushmore, Yellowstone, DeSmet SD. We ended up in NV where there was arsenic in the water.
If she is sleeping drive!!! Do not stop for anything, ok maybe gas. You will get a long way of you drive while she slumbers. When she gets cranky stop for a few minutes and get out. Car seats are hot.
Sit in back with her and read, play with toys, feed her.
I gave my kids new toys, books or something they had never eaten, 12 yo had, like gummy bears and otehr snackies.