You are getting good advice on going 13 thru the tunnels. However you will come in on the far north end of the Outer Banks. The bypass will be very congested and slow for the most part, depending on what time you hit it. When you get to the Whalebone junction (southern end of bypass) Hwy 12 bears left. Then you are on 12 for the duration of your trip. It is roughly 23 to 30 miles from that point to the KOA. Don't fret about fuel or groceries. There are two gas stations in Rodanthe with reasonable prices and a Food Lion in Avon 15 miles south on Hwy 12. They are building a new bridge over Oregon Inlet but other than a little congestion it is ok. About halfway to the KOA on 12 they are building another smaller bridge and that area needs you to be mindful of the speed limit and congestion. The temporary bridge you will cross there says 25 mph and trust me you do not want to drive much faster than that with a rv.
Have fun and be safe.