This would be worth looking at as well
IRAS: Individuals (For Foreigners)
If you're still classed as an Australian resident prehaps you would qualify for deductions from the ATO on accommodaton in Singapore and travel costs ? Definately ask an accountant for advice, it may qualify as a work related expense.
Unfortunately it looks like a pilot moving from Australia to Singapore to work for Jetstar, unless willing to establish himself and his family there on a medium to long term basis and drastically reduce ties with Australia, is going to be up for Aussie income tax.
This probably renders the present package unviable for most pilots unless substantial additions are made to cover the increased costs of a short term relocation if taking the family, or the expense and inconvenience of commuting and running two homes.