We have driven down with our daughter when she was 9mo, and many times since. A child that age has lots of stuff you need to bring with you!!! With driving you could bring whatever you need and not worry about lugging it around an airport with the baby, stroller, carseat, etc, etc. No worry about damaging things, or broken baby food bottles. We always drive and DD never has given us a hard time. Your 10 mo will probably sleep alot on the drive and you can stop at the rest areas to stretch and play. We always reccomend driving, we love it and you really save $$$$$. Having your own car and carseat while there also helps. You can drive through the night that way baby will be sleeping for the longest part of the drive, if you and hubby can stay awake driving and taking turns. Or, you can drive all day, then sleep over one night in SC or Georgia and then a shoter drive the next day to WDW. Just bring lots of toys. You could bring a cooler with drinks and lunch and have a picnic at one of the rest stops. Even though your DD will be still facing the back in her carseat, she can still look out the window "sight seeing". My DD loved looking at the cars passing at that age. You and hubby can take turns sitting in the back with her, maybe reading her stories or just playing with her.
I say go, drive and have a great time!!!