No there is no camping at the picnic area and I don't think you would want to because there are alligators on the ground.
There is a campground on the island. It's not by this picnic area. If you go to there website www.jekyellisland.com you can get a map of the island and campground.
None that I saw, but we just were there to eat lunch at picnic tables, it's a smaller area.
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