Hi George, In my humble opinion, your chances of finding a suitable place for land sailing on one of the great Barrier Reef Islands is fairly slim but I will give you a couple of suggestions here.
One Queensland Island where I am sure there is a beach suitable is Fraser Island. This island is "World Herirage Listed" but it is not a Barrier Reef Island and probably falls outside the brief of the "World's Best Job". Also this island has 4wds a plenty on the ocean side beach and is tightly regulated due to there having been a number of accidents involving inexperienced back packers driving 4wds. The beach is classified as a public road and land sailers are not allowed on public roads.
However I believe the southern 15 klm of the beach has recently been made a no go area for 4wds. This stretch of beach would be ideal from the wind angle point of view but not having been there I am unable to comment on the suitability of the beach surface. Getting there is logistically challenging to say the least.
The Island I have been to for land sailing that hillsy mentioned is Dr. May's Island. This is a tiny island about 2 acres in size when the tide is out, situated in the mouth of the Elliott River. We have been there only once and were lucky enough to have everything right on the day. The run is only about 250m long.
The next island I can suggest is Great Keppell Island. There is a beach on the southern side of it that should be ideal though limited in length. Getting there is a logistic challenge as well.
My final suggestion is Hamilton Island where I believe you will be based. When Keith Williams was in control of the Island he would occasionally have the airport shut down so that he could ride his vintage motor cycles on the air strip. This would be an ideal venue and if you can talk the relevant people in authority into it, you should enter into a sales career. You might just pull it off though. The strip may only used for commercial flights to the Island and there could only be a couple of them each day. Blokarts would be the ideal thing as there are plenty of them at Mackay and around Airlie Beach. You could contact Phil Coulter on "www.blokart.com.au" as well as the Central Queensland Blokart Club via the forum on that site. As a publicity exercise that might work. Blokarts were featured in one of the episodes of the Greatest Race I believe. Best of Luck. Cheers Cisco.