Thanks for your question.
Health care is a shared responsibility in Australia, meaning that both the federal and state/territory governments are able to make laws about it. For more information about how the federal and state/territory governments share power take a closer look here.
The way that health care is managed by both the federal and state/territory governments has developed over time, and continues to be negotiated between federal and state/territory governments. Generally, the federal government gives money to the states and territories for health services, as well as providing broad national policies on some health issues. The states and territories are more involved in the delivery of health services, such as the management of hospitals, doctors, nurses and other health care workers.
If you want more information about the areas of health care that federal and state governments are responsible for, you might like to visit their websites and compare their roles and powers.