We've done this trip 2 times...Both for Teachers convention week, or Jersey week as WDW vets call it.
One time we left at 3:30 & the other time at like 4:15. We are in Bergen County up North though, Roughly 10 minutes from the GW Bridge.
The time we left at 330 we stopped for dinner at the last rest stop on the turnpike for 1/2 hr. so this helped on that trip.
Both times we went thru DC with no problems at all, & 1 was on a Thursday, the other a Friday night.
We didn't stop on either of those trips either, I figured I'd just drive straight thru the night & we arrived before noon the next day. You should be fine because you'll be getting into that area after 7 for sure ..Have fun.