Health insurance, content insurance, social insurances - moving abroad will require some checks and changes. Some insurance policies might still be valid in Australia, often depending on how long you will be abroad. You have to check with your insurance company and may find that you have to cancel or at least to modify your insurance cover.
The Organisation for Swiss Abroad provides helpful information on OASI/DI (AHV/IV), pension fund insurance and health insurance. Also check the website of the Australian Delegates of the Council of the Swiss Abroad who frequently provide updates on the Old Age insurance.
If you are thinking of paying further into your OASI/DI (AHV/IV) note that you have to meet the deadlines. Further information on the voluntary OASI/DI is available on the website of the Central Compensation Office.
In relation to health insurance, Medicare is the Australian public health care system for citizens and residents with permanent visa. Immigrants on a temporary visa may have access to Medicare under certain circumstances (e.g. Visa covered by ministerial order, citizen from a country with a reciprocal health care agreement). If you are not covered by Medicare, some of your 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).