Permits are required for both driving and camping on Moreton Island.
Native Title of the Quandamooka Yoolooburrabee group was formally recognised on Moreton Island on November 22 2019. This means that all vehicle access permits and camping permits are now booked through the Quandamooka Yoolooburrabee Aboriginal Corporation (sometimes called QYAC) on their website here: https://www.mulgumpincamping.
You can also get in touch with them on (07) 3506 2371.