Medicare is the Australian public health care system for citizens and residents with permanent visa. Immigrants on a temporary visa are not eligible to access Medicare, unless their country has a reciprocal health care agreement with Australia - which is not the case for Switzerland (as per 1/4/2017). Hence Swiss with a temporary visa are not eligible to access Medicare. Their options are:
There are advantages and disadvantages with either solution so you have to check what suits you and your family best.
Positives about insurance with an Australian provider are:
Be aware that waiting periods apply to your cover, especially for pre-existing conditions and pregnancy/childbirth (see for example BUPA).
Note that when applying for Visas like a subclass 457 visa, you must provide evidence of having arranged an insurance policy that will cover you and your accompanying family members in Australia.
CSA Oceania, the council of the Swiss abroad delegates for the Oceania region have a website! Created in October 2016 to improve information exchange and be present as delegates online.