Not sure if its the quickest but you could take the Jersey turnpike then over Del Mem Bridge then follow Rt 1 to RT 113 OR Rt 13 all the way down to the CBBT then around Norfolk to Outer Banks, or use the Garden State Parkway and take the Cape May ferry then south on 113, but the ferry will be very pricey towing a trailer.
2004 Chevy 2500HD Crew Cab 6.0l, 4.10r
2010 Jayco Jayflight 28BHS
Reese Strait Line with Dual Cam
P3 Brk controller