If you are relocating the United States, it is important to know that the US does not require all expatriates (or US citizens) to have medical coverage. However, the risk of being in the US without medical coverage is massive hospital bills or even no access to medical care. There are newer requirements for certain expats on select visa types that may require you to have health coverage.
Most aspects of private health insurance in Australia are regulated by the Private Health Insurance Act 2007. Complaints and reporting of the private health industry is carried out by an independent government agency, the Private Health Insurance Ombudsman. The ombudsman publishes an annual report that outlines the number and nature of complaints per health fund compared to their market share 
Health insurance in the United States is any program that helps pay for medical expenses, whether through privately purchased insurance, social insurance, or a social welfare program funded by the government. Synonyms for this usage include "health coverage", "health care coverage", and "health benefits". In a more technical sense, the term "health insurance" is used to describe any form of insurance providing protection against the costs of medical services. This usage includes private insurance and social insurance programs such as Medicare, which pools resources and spreads the financial risk associated with major medical expenses across the entire population to protect everyone, as well as social welfare programs like Medicaid and the Children's Health Insurance Program, which both provide assistance to people who cannot afford health coverage.