We were there last October. We drove all the way to stay at the state park right on the beach only to find out they don't allow pets because of the horses in Assategue which is where you're thinking about. You can travel a little further south and stay at Chinoteque, but didn't go there at all and can't comment on it. We finally settled on a campground called Frontiertown.
http://www.frontiertown.com/ It wasn't all that bad tho we were at the end of the season when we went. They did have a lot of activities, a waterslide and a few other things for the kids, and even had two buffalo wandering around at the entrance! The campground was pretty clean. Yes, there were a few "full time" sites there, but not anything really bad. They had their own store, but it had been in a fire the week before, so it wasn't open, but probably is now. They come by your site a few times a day and pick up your trash for ya via golf carts, just leave it in the bag next to your site marker, and they'd get it np. The site we got had full hookups, including cable and maybe even telephone. The site was spacious it seemed, and included a picnic table and fire ring. And YES, they allow pets. There are a few jeep trails there, but you have to pay by the day, or for the season. It was a lot like the outter banks, but seemed like too many rules in MD, that I wasn't very pleased with it. In OBX, you can take your TV right out on the beach and tailgate right on the beach! But Frontiertown wasn't so bad, even in the off season, and plenty of stores right close by as well........
[glow=red,2,300]Happytrails......[/glow]