Anybody can teach in a private school if they want to teach in a private school. It's a separate application process to the board that runs catholic and independent schools in your state. It doesn't matter where your degree comes from. It does help if you have some kind of proven background with your faith and that you take the whole faith thing seriously. It may also help if you have "a mate" that works inside the catholic school system that can give you a good word.
I never taught private on principle. Firstly, I don't want to have to sit through mass. Secondly, the compulsory religious classes that come with private school life don't agree with me. Thirdly, I believe in equality on principle which means not spending public money on private schools. But each person has their own views on faith and this will be one of the determining factors for each applicant once they've finished their degree.
It really doesn't matter where your degree comes from so long as its an approved education degree. If you want to go and study religion specifically for teaching it in schools then ACU might be your gig. There is a university up the road called the University of the Sunshine Coast which has a really well recognised education program these days.
It doesn't matter though where your degree comes from. It used to be QUT for education a long while ago in Queensland. These days there is that little difference in it it really does not matter. That is, unless you want to become a specialist religious teacher in which case ACU might be your gig. This is because not all universities will offer the nescessary coursework to have the nescessary major/minor in that area.
Do be aware if you do decide to study religion at university it will REALLY limit your degree value if you do decide that the whole teaching thing is not for you. You need to think about what your fall back idea is if the teaching thing doesn't work for you. That's fine if you want to become an academic in that particular area, or if you want to become a church minister, but it's not really a useful major/minor to have otherwise.
That's not meant to belittle people who want to study religion at university, but you really have to weigh the full consequences up with the decision about how seriously you take your faith, and what will happen if the first option does not weigh up the way you thought it might.
I really wouldn't put value in university rankings especially not for newer universities in particular, they're skewed for a myriad of reasons. In terms of teaching in Australia, it does not matter where your degree comes from so long as it is an approved education course. I am not aware of any university in Australia that offers a 3 year (undergraduate) or 1 year (post graduate) teaching degree any longer that are not approved.
The only reason why university rankings would matter is if you plan to teach overseas at some point in your career. You will have an equal footing regardless of where your degree comes from otherwise.