The government should not be providing private schools with one cent of funding, let alone the current situation where the federal government provides more funding to private schools than it does to public.
It isn't explicitly that the government (whether it is state or Federal) is giving money to the schools, it's the students that are funded. Every kid in Australia is entitled to $x per year in education funding. I'm the product of public schools, and my kids also go to public schools. But, I don't begrudge people the choice of sending their kid to a private school also getting their $x in government funding. They pay their taxes, they are entitled to the funding. It gets a little more complicated than this, as schools get funding for major upgrades like new libraries etc.
As to the argument on whether people should get government funding if they elect to send their kid private, that has precedence. For 100 years, the private schools lost government funding and were on their own. In the end, that lead to the Golburn School Strike. The government agreed that it was in no shape to actually take the 36% or so of students who attend private schools.
Yes, the federal government does give more money to private schools than it does to public: That's actually been a bit of a cherry-picked statistic. This is because most of the public school funding has been coming from the state governments. At least, to now. If all the states sign on to this, we should see some transparency on this matter.