Jag hittade detta och det verkar som om du har rätt till Medicare omdu är svensk medborgare vilket jag antar du är:
You are entitled to full health insurance coverage under Medicare if:
You are an Australian citizen You are a permanent resident of Australia
If you are living in Australia on a temporary visa, such as a 457 visa, you may or may not be entitled to limited coverage under Medicare. Some countries have reciprocal agreements with Medicare, which means that citizens of those countries living temporarily in Australia are entitled to Medicare coverage, and Australians living in those countries are also entitled to coverage under the national health insurance system, hence the term ‘reciprocal.’
The following countries have a reciprocal agreement for healthcare with Australia:
United Kingdom
Sweden Finland Norway The Netherlands Malta Italy
If you come from one of these countries, you are entitled to treatment that is medically necessary whilst you are in Australia. This includes visits to doctors, in-patient and out-patient treatment in public hospitals, and drugs subsidised under the Pharmaceutical Benefits Scheme (PBS). It does not include dental treatment.
If you are from the UK, Sweden, Finland, Norway or the Netherlands, you are entitled to treatment for the whole of your stay in Australia (i.e. until the expiry date of your visa). If you come from Malta or Italy, you are only entitled to coverage for the first six months of your stay in Australia.