Try to leave aroud 3:00am, take 84 to 87, at that time of the day you can take it right to the GS Parkway, follow that to the NJ Turnpike. Take that South into DE and get on 95. Follow 95 south into Baltimore. Take the Harbor Tunnel, then get onto 295 (B-W Expressway) follow to 495. Take that around DC, regardless of the time of day there will be some traffic in DC, but you should be there at about 7:30, maybe 8:00 so it won't slow you down. Go over the bridge, pick up 95 south, take that down to Richmond, use the bypass (295) much easier drive, get back on 95 and stay on it to Daytona, where you'll pick up I-4 which takes you right to WDW.
Should take you 18-20 hours if you don't stop too much and don't hit a wreck or Nascar traffic anywhere.
Here's a note on potty breaks...The restrooms in the service areas in NJ, DE, MD are fairly clean and safe. Use the restroom in MD before you get to Baltimore, there isn't another until you are south of DC in VA. Stony Creek, VA (exit 33 of I-95) has a great clean travel center with clean restrooms and both Starbucks and Krispie Kreme. We almost always stop there to gas up and get something to eat.
The rstrooms in the rest areas in NC are generally clean and safe. SC and GA rest areas always made me feel uneasy, and many of them are gross.
The FL rest areas are pretty safe and clean.
I have made that round trip drive from Central NJ to FL half a dozen times in the past year (2x in teh past three weeks), and would be happy to answer any questions.
Anne