Yes, Medicare surcharge of 1% kicks in around $80k for a single and $160k for a family.
There is also the Lifetime Health Cover (LHC) reduction which aims to encourage people to take up private insurance at a younger age (31yrs). The older you are when you take it up, the less you get back from the Government. There is exemption from this for recent migrants, who are treated as if 31yrs for rebate purposes as new migrants.
However, this is all under discussion by Governments and rules liable to change pretty soon.