Now I was wondering: If one inverts so much money into such a RADAR on the mainland, then wouldn't it be logical to take advantage of the location of Cocos (Keeling) Islands to dramatically extend the range
There are two radars (plus Jindalee, the prototype) about 900 miles apart. Each has a Tx and Rx array about 1/2 mile long separated by about 50 miles. JORN also relies on transponders along the coast to provide real time data on the ionosphere. These are typically 500+ miles from the radar arrays.
Jorn is BIG. The Cocos archipelago is only about 5 miles across.