we have the Special Flight Permission from the other country so as to make it Airworthy for the purposes of this flight
I am guessing you have that for an overweight takeoff.
You will not need a special flight permit, that is for VH registered aircraft. You will need a special flight authorisation under CAR 1988 135A which allows operation of a foreign registered aircraft in Australia that is operating on a special flight permit or a special certificate of airworthiness issued by a National Airworthiness Authority (NAA).