We are west of Philadelphia, so our timing is very close to yours.
We like to leave at 9 am and avoid ALL the rush hour traffic everywhere. Then we drive until 11-12 pm, which puts us at Savannah GA. Then we get up, have breakfast in the hotel and leave for WDW by 9-10 am. It's around 4-5 hours from there to WDW, so we get there right at check-in. Plus we get to stop at the Florida Welcome Center and get our free juice and load up on the Disney brochures for the "excitement" build in the van for the last few hours.
Take 295 around Jacksonville. And I'd also recommend 417 off I-4 to Disney World. It's about $7 - $8 in tolls, but is so much less crowded and does not go through a major city, unlike I-4 which goes through the center of Orlando, full of idiot drivers - both locals who are annoyed at the vacation folks, and the rental car drivers.
We have tried to leave at 4 am and that has been fine, but we don't like to drive for 15-16 hours, we find we are too tired and worry about the safety of us and our kids. So we take it as far as we feel we can handle. There's nothing worse than exhaustion and knowing you still have a few hours to drive. We tried it once and my eyes were crossing, and I was in the passenger seat. I would never be able to drive that long.
Welcome to the thread! It's the best one on the DIS!