We went to DC last year (and HHI this April). For DC we made the mistake of leaving our house at 11AM (Central NH). We got stuck in the NY/NJ traffic and the NJ Turnpike was a nightmare! It took us 14 hours total (and should have only taken 9-10)
For HHI we left home at 4AM and picked up my sister in Brighton MA and were back on the road by 6AM. This worked much better.
Either way, I suggest going through Hartford, over the Tappan-Zee and down the Garden State Parkway to the NJ Turnpike, a bit of a roundabout....but it saved us a LOT of traffic headaches the 2nd time around!
So really I have no good advice, if you can leave any time after 7 I guess that I would take off right then. On a Friday traffic could get hairy in NY, so if you could get through that...hopefully the rest could be smooth sailing.
Good luck!