Take some good bug spray, as the spring hatch of skeeters and flies should be out by then!
If you have time for more leisurely drive up north, a nice way to go is to take the free vehicle ferry from Currituck, NC, to Knotts Island, NC (at the southern tip of Virginia Beach). Currituck is right off the main route north from the Outer Banks (158). See http://www.knottsislandonline.com/travelguide/ferry.htm
Then take US 13 across the Chesapeake Bay Bridge Tunnel, which is a neat drive. If you are lucky you'll catch some ships from the US Atlantic fleet putting to sea from Naval Station Norfolk, or maybe see some SEALs running training ops in their small rubber boats. I believe you can free camp overnight in the large rest area at the bridge's northern end (I've seen campers there many times) if you want to boondock. The bathrooms are open 24 hours, too.
Taking US 13 north is a few more miles than going via I-95, but actually is usually faster because you miss all the DC, Baltimore, etc., traffic. It's also a lot more relaxing and scenic, going up the DelMarVa Peninsula. We used to live in Va Beach and would drive back to Philadelphia all the time, so we have tried both ways.
Chincoteague NWR is a short detour off Rt. 13, and then you can branch off Rt. 13 onto Rt. 113 to Assateague Island National Seashore, which has nice oceanfront and bayside camping. There are also a number of very nice Delaware state campgrounds up the coast, with Cape Henlopen State Park being one of the nicest.