Yes, you do indeed need ambulance cover, preferably asap, as you never know what will happen. We prefer to use SA Ambulance http://www.saambulance.com.au/Produc...anceCover.aspx
as they provide full cover and although you can get cover through your Health Fund it is often emergency cover only.
Health Insurance is available from several Funds and they cover hospitalisation in a private Hospital and any extras you choose to be covered for. They do not cover any Outpatient visits to doctors or procedures, whether in a public or private hospital.