My understanding is that under Aussie law, you're paying tax twice. Both in Singapore AND Australia.
The EXCEPTION is if you declare yourself no longer an Australian resident, then you only get taxed by Singapore. (nothing stopping you then later 'changing your mind' and moving back to Australia to take up residency again)
But like anything, get professional advice from your accountant.
edit: if by chance you DO declare yourself as a non-resident of Australia, and still derive income from Australia, eg you have
property you are renting out to tenants, or you earn income from bank interest, shares etc... you are no longer entitled to the tax free thresh-hold back home, and you're taxed differently as well..... so do weigh up which option is best for you paying 2x lots of tax on your 'job', or higher tax on your supplementary income.