We have a child's booster seat for my son, who is a few months shy of his 4th birthday but, who has already outgrown his carseat.
I don't know what the laws are state to state, but, I thought that children under 5 have to be in a car seat/booster seat. I'm not saying this to be snotty or mean, I just don't want to see anything happen to your granddaughter. Also, if for some reason you get pulled over on your long trip down, if the law is different from one state to another you might be involved in a serious situation.
I would get one of the booster seats, they sell them for as low as $30.00-$40.00 at Wal-Mart, K-Mart, etc.. Then I would just get her a neck pillow or bring a pillow from home.
Have a good trip, we're driving from Illinois is 4 days!!!!