Apple Watch Series 4

No.

The radio frequencies are different.

Here is a list of cellular carriers that support the Apple Watch. Pay attention to the model numbers and the radio frequencies supported.

https://www.apple.com/watch/cellular/

A regional carrier will not try to support a limited subset of frequencies that may overlap, so get an Apple Watch that is designed for your region and your cellular carriers.

NOTE: A GPS ONLY Apple Watch will work anywhere that your iPhone works and give you all the same functionality as the cellular model as long as your iPhone is nearby. The cellular model gets to leave the iPhone behind while you go for run, bike ride, etc... and still make/receive phone calls, stream Apple Music, send messages/text.. The GPS model can play stored music, and track run exercise.

Please read the following webpage and pay attention to the footnotes to understand the differences between GPS only and cellular models

https://support.apple.com/en-us/HT205547

You should check the Australia carrier if they will support your Watch. But technically it should work.

NOTE: your warranty may not work, except if you go back to Singapore. Since the watches are regional, I do not think they have an international warranty.

I am mostly speculating, so you should check to make sure.