Yes, Australian government does provide free or subsidised treatment by health professionals such as doctors, specialists, optometrists, dentists and etc. There are also free treatments and accommodations in public hospitals, which are covered by the Medicare (the Australian Public Health System).

You are eligible for Medicare benefits if you are Australian or New Zealand citizens or are permanent residents in Australia. As with the public health systems in other countries , there is always a long waiting period. For more about Medicare, check the official information here.