Hey mate,
Not too sure about the medicare and what you are/are not entitled to on your visa. Everybody pays a medicare levy (1.5%) of their income, basically a tax. If you earn above a certain about (think it's about $80k at the moment, not $180k as stated above) and do not have Private Health insurance (PHI), you pay an additional 1% of your income (Medicare Income surcharge levy). If you are not entitled to Medicare you can get a cert to be exempt from the levy.
Regarding PHI, you are encouraged to take it out from 30 (ie penalised if you do not have it). There are 2 types of PHI with many different levels of cover, Hospital and Extras/Ancillary. Often sold as a package but are 2 separate products. Extras covers Dental, Physio etc with different limits depending on your plan - Govt aren't concerned about this at all. This is a lifestyle product and you should claim as much as possible
Hospital is the product you hope you never have to use (ie you get sick, need an op etc), it covers hospital admissions, protheses etc. Again, different levels of cover depending on your product. This is the product that determines whether you pay the surcharge or not. It basically enables you to skip the q and choose your own surgeon/consultant etc. Depending on your income level, you do get a tax rebate on your premium up to 30%. The PHI will refund this to at source if you like (ie reduce your premium)
If you have hospital cover from the age of 30, you just pay the premium. For every year after 30 you pay a 2% loading on your premium for 10 years, eg you first take out PHI at 35, you will pay a 10% loading on your premium for 10 years. Now if you are a recent migrant to Australia, you have some time to take out PHI without being penalised, I thought it was 3 months but it may be a year. Eg. you move to Australia at 60 and take out PHI within the 3 months/1 year, thay effectively treat you as taking it out at 30 (effective age for loading purposes). PHI insurers often get this wrong, you need to prove that you are eligible for this. Bupa charged me a 6% loading for 5 years, I moved to HCF and realised I shouldn't have been paying the loading at all. I did get a refund from BUPA once I got the right paperwork together.
PHI does not cover GPs as a rule. Medicare will cover some or all (bulk billing) depending on your doctor.
Clear as mud? Hope this helps