How to use ECG function with an Apple Watch in Australia?

According to this, watchOS - Feature Availability - Apple ECG is not yet available in Australia. See the information provided here in regards to using the ECG app and the Apple Watch. Taking an ECG with the ECG app on Apple Watch Series 4 or later - Apple Support

If you wait, you will get a response from an Apple rep providing you additional information and a link to Apple regarding the ECG. You will find that delays are due to government issues, and the government health authorities have not approved the device as a medical device. That is what is holding up the changes. The release of watchOS6.2.5 and iOS 13.5 just brought it to another country, so it moves, slow but sure. Government bureaucracy, that is how it works.

If it will make you feel better.

NZ only recently got the cellular model and is supported only by1 carrier.

OZ has all the cases and models available like in the U.S., whereas NZ has only 2 choices: Aluminium or Stainless Steel

No on both questions.

Yes seems like there's a road block.

Note: Since ECG is considered as a medical device, it need approvals from the health authorities.

FYI: NZ just got theirs only recently.

Good luck.

Well, I have the Watch Series 4 since 2018 and still waiting.

Got my wife a Series 5 in 2019 and hoping.

Anyway, it's still very useful without ECG.