Moreton Island is the third largest sand island in the world and quite aptly has a large area on the island known as "The dessert". It's the area the bus will take you if you choose to go sandboarding but it's walking distance from the resort (it's a bit of a hike) and makes for a great experience to get caught up in by yourself.
The walking track to get up there is down the south end of the beach, over the logs 2-300 metres on your left. For more accurate directions you can ask at the reception and they'll point you in the right direction.
The walk up and back takes about an hour and a half and there are plenty of sites to see on the way.