Australia's health care situation is quite "similar" to Malaysia's in the sense that you can choose to buy health insurance coverage, or rely on public health care service. The difference is that Australia's public health care service is by far much better than Malaysia's. Unless you are in the high income bracket, you can safely rely on the public hospitals. Even insured people are ultimately referred to the public hospitals as a final recourse (unlike in Malaysia where many will turn to Pantai Hospital or SJMC if they have the means).
Sign up for a Medicare card as soon as you can. Then you can visit clinics that provide "bulk billing" and you won't need to pay a cent for consultation. If you are referred to a non-bulk billed place for further tests or consultations, you can still get partially reimbursed by Medicare. If you are hospitalized, you are also covered.
Ambulance service is not free. It is best to sign up with Ambulance Victoria as soon as you arrive. You can do that in a post office. You'll never know when you need one and it is very expensive to call for an ambulance.
Dental care is very expensive. A simple filling for a cavity can cost you ten times more than what you pay in Malaysia. It is not covered by Medicare. Plan your treatments to be done in Malaysia if you go back regularly. Or else, buy a "comprehensive extra" coverage, which costs $1k+ per year, and will provide you some peace of mind. Note: this is not hospital coverage. It is only for things like dental, optical, physiotherapy, etc.
Finally, if you intend to buy health insurance coverage anyway, do so within one year of your first arrival. Then you won't be penalized with a hefty premium loading.