My wife and I are planning to fly from Melbourne Australia to Singapore

If you will fly to a third country or region rather than the last one you come from after staying in Shanghai for not more than 144 hours, you will qualify for the 144 hour free transit in Shanghai. When you board the ship in last country, you should inform the cruise ship company that you want to use the 144 hour free transit in Shanghai. After arrival in Shanghai, you need to go to the immigration office to apply for the 144 hour free transit.

Thank you Julie,
would flying from Shanghai back to Melbourne Australia qualify as the third country or region?
Being Australia, Singapore, Shanghai return to Australia.

In this case, you will be able to enjoy the free transit in Shanghai.