Hi C.!
I have traveled several times with a little one, and it can be fun if you plan it right. My dd and I traveled from Lafayette, LA, to Searcy, AR, six times the year she was two. It was a little nervewracking, but we made it! I agree with several other posters, SNACKS, SNACKS, SNACKS! I always took goldfish, fruit snacks, several sippy cups full of milk or juice (in a small cooler), even some of her favorite candy. If you take several cups already filled it will save you from having to pour liquids while you're trying to drive or having to stop just to fill a sippy cup. We had a DVD player, and that helped a lot. My daughter was a movie junkie, so I was lucky. She also loved to color. I usually brought a blank pad of paper and a coloring book or two. The magnadoodle was great, too, especially since the pen is attached and she didn't drop it.
It's rough to go that far in one stretch. Stopping to spend the night might be a good idea. My dd loved it when we stopped at a hotel with a pool. It was a nice break for her.
If you do decide that it's cost effective to fly, you might check out this website:
http://matrix.itasoftware.com/cvg/dispatch/
This will show you most of the flights that are available and what airline they're on. You will have to go to the airline's website to book, but I have found some fabulous fares on this place. If you need some help looking for airfares or booking just send me a PM. I do it all the time and might be able to help you find something that's within your budget.
Good luck!
S.