Hi, Korina! The crowds are usually beginning to thin out by the end of August, although you will notice that the offer of free dining does keep things hopping! You definitely won't see crowds like you will in the middle of summer or during a holiday, and it should be fairly manageable for you.
We drive down from New Jersey on almost every trip. There are several things we do to keep our kids entertained. We always have a stack of DVDs and a portable DVD player for them to watch some of their favorite Disney movies. I try to pick up a few new ones - even if they are old movies that are discounted at Walmart or even the dollar stores.
I keep a stack of coloring and activity books in my closet, and each trip, I pull out a new one with a box of crayons. Now is a great time to stock up on those things with the back to school sales everywhere!
We keep snacks and drinks in the car, but we plan stops to make sure everyone gets to stretch their legs. We also have a rule in our car - if Mommy's going potty, everyone is going potty. This helps cut down on multiple stops that can delay your trip.
You can also find small toys that your little one might enjoy from the dollar store that will keep her busy. My girls love getting new little surprises each trip!
One thing that works for us is driving as much late at night and early in the morning as possible. With the kids asleep, we seem to get much further much faster. No extra stops required for sleeping kids!
Have a great vacation!