WoodWoseWulf
This is a weird one.

The nature reserve is listed as Moon Island Nature Reserve on NSW National Parks:

http://www.nationalparks.nsw.gov.au/visit-a-park/parks/moon-island-nature-reserve 

But... on many other resources, the actual name of the island is listed as Green Island.

Regardless, yes, it is a real island, but I don't know what its actual name is (maybe one needs to be an Alt_Name for the actual landmass?). Boat landing is forbidden and it is a seabird breeding sanctuary.