Mmmmm .... Good Luck mate!
I suspect all the operators of twins would only really be interested in (new hire) blokes who have also got instrument experience as well.
You will have to try Bristow Australia, CHC Australia, Helicopters Australia, Jayrow Offshore and possibly Australia Helicopters to see if they are interested.
Also try to get the Friday edition of "The Australian" newspaper which carries an aviation supplement with some employment opportunities listed. Also you can try
www.afap.org.au (Oz Federation of Air Pilots) .... usually on Fridays from say 1200 hrs Oz time to see what jobs might be listed .....
Cheers