Hi! We've done this trip many times over the years....We always left LI early to beat the city traffic....Wanted to clear the Verazanno by 7:00 or so...Smooth sailing from there! We never drove straight through, always made an overnight stop in NC or SC, having made ressies in advance...except one time. The distance is about 1100 miles and takes us approximately 19-20 hours, including a bit of traffic here and there.
One time we thought we'd drive as far as possible and started to look for a room in GA. Well.... it was the week of Daytona 500 and we could not find a room between Savannah and Tampa. We slept in the truck! After that experience, we always charted our course and made a hotel ressie.
Driving now costs us much more than flying/rental car since my DH is self employed...He'd rather spend those missed days at WDW than on the road. We now fly but I really miss the old days of driving to WDW with the family.
Have a safe trip!!!