Moving abroad has consequences for your insurance scheme. 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.
As for Social Insurance, the Organization for Swiss Abroad provides helpful information on OASI/DI (AHV/IV), pension fund insurance and health insurance.
If you are thinking of paying further into your OASI/DI (AHV/IV) note that you have to meet the deadlines.