Hi Lisa -
We just came back from Disney on August 11th. We drove down from eastern Pa. We left on Friday, Aug. 2nd. The first day we left our house at 4:56 a.m. and got right on I-78 which is only a block away. We stopped only twice to get gas and our total stopping time was 30 minutes. We got to Savannah, Ga. at 4:50 p.m. Of course my daughter is 20 and my son is 16, so that makes a huge difference in your stops. We had to stop for longer periods when they were younger. At any rate, we stayed overnight in Savannah and then hit the road the next day at 8:33 a.m. (i have a record we kept of the exact time we left, when we reached certain towns, etc. for future reference

, anyway, we left at 8:33 a.m. and reached Exit 67 to Epcot/Downtown Disney (we were staying at Old Key West) at 12:47 p.m.
This is the third time we drove down - the first time was in 1994 when my DD was 12 and my DS was 8, the next time in '98 DD was 16 and DS was 12. We always leave early in the morning - I am just not good to drive at night - I get hypnotized by the road and it's too long of a drive for one person. My daughter helped drive this time and hopefully my son will be able to also drive next time, so with 4 drivers, we are thinking of driving straight through.
At any rate, you know your own kids - if they get bored easily, if they will sleep some of the time, what it takes to entertain them. One thing we did have the other two trips was a vcr/tv combo my husband put together. We took some of my kids favorite tapes and just watching one or two tapes sure did help the time pass by more quickly. I believe somthing like that can be rented or purchased as well, but it will be much more expensive.
Whatever you do, enjoy! And just be safe! One thing I saw during the day was traffic moving at 80 - 85 mph constantly. Thank God we didn't see any accidents, but a lot of "near-misses", that's for sure. It is a tiring day, there is no doubt about that - but I have to say our trip went more smoothly this time than it ever did before - we had no problems with construction or hold-ups of any type. We just kept on moving with the rest of the traffic and made really good time!
Good luck!
Paula