From memory you used to be able to camp at a couple of spots, Scout Park I think, can't remember & maybe Direction Island.
Scout Park is nice but the mozzies would kill you and there's very little water on Direction Island.
You could say you just arrived from Sri lanka and you will get free accommodation for a week at the Quarantine Station, they even chuck in meals and someone to hang around with, then a free trip to Sri lanka with the whole plane to yourself