Hi there. we are in Howard County & DH used to work in DC. He retired in the fall and we've driven through there at all hours of the day and night.
At four am, you'd think the traffic would still be light but it's not. You have early commuters, then also have to account for construction. If you leave your a area at 0400, you're going to hit rush hour - because you're driving towards DC along with thousands of others trying to beat the rush.
Are you planning to take the 495 beltway or drive down 295 through DC to continue onto 95? I'm not sure where construction is going on right now but we ALWAYS have construction here.
If you can do the straight shot, I'd do it. You're probably an hour north of me, so you'd want to leave around 9pm (2100) - if you and your DH can alternate the sleeping/driving, that is.
Also, the area between DC & Fredericksburg, VA, no matter when we hit, has perpetual traffic. Later in the night has been better for us.
It might be helpful to make a specific post for Northern Virginia & maybe folks who live there & travel it daily can be helpful, too.
I'm too neurotic to break it into two days to get down there - I'm too amped up and excited. We've done that twice because of the dogs and it was DH's idea, but to me, it dragged on too long.
I wish my dogs could fly with us but at 100 lbs. each, they can't fit under the seat, LOL. I love it when someone stays home to watch them so we can fly.