Thanks for your information guys. I have just finished a 2700 km bike ride east from Perth to Peterborough, South Australia, and next July/Aug will use the same bicycle from the Tip, south to cairns.
Flying with the bicycle to
Horn (sorry for the typo) Island seems a lot faster and less expensive than taking the boat from Cairns to the Tip.
My strategy is to follow other bicyclists suggestions: from
Horn Island take the Macdonald's ferry to Thursday Island and then the Peddell's ferry to Seisa/Bamaga. Then after arrival in S/B I will walk to the Northern Tip and will start the bicycle trip south to Cairns.
I have taken that bicycle a number of times (overseas and domestic in Australia) in both the Qantas bike box and in Air Canada-supplied bicycle bags. All have worked out well so far. After all, it is a for-expedition built bicycle with steel frame, etc...
In checking the schedule, on the dates I am interested in late June/early July 2016, the 1st flight leaves MEL in the morning and arrives on
Horn Island in the late arvo. There seem to be 3 flights: first 2 by jet and the last from Cairns to
Horn island on the DH-8. Qantas will worry about losing the bicycle, og. I am NOT going there. Thanks for your concerns,og,
BUT please read my comments about the bicycle on previous air-travel (previous para).
Good info everyone. Thanks for the info ^ and your cautions...

Sorry for the typo of
Horn island - my bad

and