Many years ago (late 70's I think), SQ chartered the concorde to fly between London & Singapore, stopping at Bahrain. It ceased a short time later as countries were not tollerant of the sonic boom caused by the supersonic airliner.
Today the same applies, it is also very uneconomical to fly Concorde over such a distance with only 100 or so pax. The only market that can really sustain Concorde is LHR-JFK, & that has been proven by BA pulling Concorde out of Washington-Dulles & Miami. Air France also only operate (to my knowledge) their Concorde's between CDG & JFK.
Concorde will still & does operate charters to Sydney (& usually Auckland or Christchurch) as part of fly cruise type set ups, however you will never see it fly commercially or scheduled service to Sydney or Melbourne.
I will stand corrected if I am wrong, but this is my understanding!
Cheers - & I look fwd to flying Concorde one day myself!
Ansett Australia - (was) One of the worlds great airlines!