The requirement for health insurance depends on the type of visa application. Certain visa applications require you to have health insurance at the time of applying. When other visa applications are submitted, it’s allowed that you obtain health insurance later. Once you get the visa it may also be needed that you maintain the health insurance through the whole period of your stay in Australia.
In fact, when you arrive in Australia, it’s your financial responsibility to meet any health care expenses you incur there. Australia provides Medicare health insurance facilities to Australia PR.
If you have no Medicare eligibility, it’s strongly recommended that you arrange for private health insurance. You can do this even if it’s not mandatory while applying for an Australian visa. This ensures that you have full coverage in case you meet with an unplanned instance involving the need for hospitalization or medical care in Australia.