Done this trip several times and no matter how fast or slow your are travelling, you will always average 50MPH.....That means that 400 miles will take you 8 hours, which for me is about my limit these days.
This will get you to Rocky Mount (just) for the first night and just south of the Florida border on the second night - so plan accordingly. We usually stay at State parks along the way. 
You may want to check out 301 instead of I95 to get you through Delaware/Maryland. Once you're south of Fredickburg, the driving gets easier.
Having said that - what's the hurry? take a an extra couple of days to see the sights on the route...
Gerry