U said u only got your FULL Singaporean on December 2008 aye? I dunno how the system works in Singapore but do you have like a P or something before your full license? cz If you do have driving experience on P's you can add that time on to your Singaporen full license, with that being said you maybe still qualified to convert that over to a full license in NSW and I m pretty sure about that ...however you will need to find that license as a prove though...
My guess is that once you have obtained your Australia license, your international license would not be valid to be used in Australia anymore...but I do think you will be fine using your QLD full license and driving a turbo car...