The short answer is, if you have adjusted taxable income (referred to as income from hereon) of over $100 000, then yes!
Firstly, almost everyone pays the Medicare Levy of 2%. This is pretty much unavoidable for Australian residents unless your income is $21 980.
In addition to the Medicare Levy, if your income is over $90 000 (or $180 000 for families) you will be charged the Medicare Levy Surcharge (MLS) when you lodge your tax return.
The MLS is based on your income as per the table below:
NB: The family income threshold is increased by $1500 for each MLS dependent child after the first child.
You can get basic hospital cover for around $1000 per year. If you are single and have adjusted taxable income of $100 000, you will pay the Medicare Levy Surcharge of $1000; the cost of the hospital cover and the MLS are the same.
If your income is over $100 000, you will pay more in tax (MLS) than the hospital cover would cost you, so it is worth looking into getting hospital cover.
If you require any assistance regarding any of this, please feel free to send me an email, I am more than happy to help.