We're a little north of Philly and have made the drive numerous times but we usually leave in the morning. One trip -- due to a bunch of unexpected things -- we ended up leaving around 12:30 p.m. and hit DC at about 4:00 on a Friday. I can tell you that you *don't* want to do that!

It was stand-still traffic and took us hours to get through the DC/Baltimore area. We listened to traffic reports and they kept saying "no accidents, just typical Friday evening traffic". I would plan to get to DC after 7:00 or so. Or if there's any way you can leave by late morning and can be through DC before 3:00, you should be ok as well. Otherwise, I'd take a more inland route and avoid the area completely.
As far as travelling through the night...we've never done that because: 1) We're not used to being awake for 24 hours straight or being awake during the night. We don't feel we'd be alert enough to drive safely. We also prefer that both the driver and the "co-pilot" are awake at all times. Our son and his wife used to work night shifts so they decided to try the straight-through drive. They said they'd never do it again -- that they were exhausted and their sleep was disrupted for 2-3 days. And, 2)
Disney vacations are tiring enough. The last thing we want to do is arrive exhausted. We've actually started spreading out the drive down over 3 days on the way down: Driving from about 10:00 a.m. - 6:00 p.m. on day one; day two we drive until we're about an hour away from Disney; day three we arrive at Disney at about 10:00 a.m. and hang out at the resort and spend a few hours at a park. We used to do the drive over 2 days as well -- doing about 12-13 hours the first day and then having about a 3-4 hour drive on day 2. This method also allowed us to get a good night's sleep on the drive down. I know a lot of people do the straight-through drive, but it just doesn't appeal to us. YMMV.