Just to translate this a little, my understanding is that you want to use Avios to book Cairns to Hamilton Island on the Barrier Reef, and Expertflyer shows you availability. Without having the dates this is going to be a wild guess but my suspicion is that there aren't direct flights between these two airports, and you therefore need to change aircraft (e.g. in Brisbane). BA.com isn't very good on connecting flights off its own metal for various reasons, so you may get more to show up if you break it into segments (and I can see CNS-BNE availability as well as BNE-HTI availability on 17 June). Then, to get it as one booking you best call up to protect the end to end journey. There is a bit more information on this in post 2 in the Sticky on How to Use Avios on the front page.