The Australian government pays for the research study fees.
Who will, in such case, have the intellectual property rights for the research: the PhD student or the university?
Laws vary and I am neither a lawyer nor Australian. But in general, unless the grant or university rules say otherwise, things you create are (or at least should be) your own. Some universities try to make a claim (various places in the world) and you may have signed away some of your rights previously, but in the absence of that the IP is yours.
Check locally for the correct answer, of course. If the rules seem arbitrary or unfair, you can explore, locally, what it would take to counter them.
As with most things when it comes to the question of intellectual property (IP) ownership, the question to ask is: Who is paying you to do the work?
If it's a general PhD stipend scholarship from the government then the default position is that the student owns all the IP and the project is classified as a "Student Project". Some government contracts may have a clause which stipulates that, if challenged (i.e. in a court), then the government provider will have the final say on IP ownership, however this is extraordinarily rare. In the case of a Australian government scholarship, I believe you can be assured that you own the IP as a student.
If your stipend is funded by an external company or cooperative research centre (CRC), chances are your PhD project is classified differently. As examples, the university may declare your project is a "University Project" or "External Project" as opposed to a "Student Project"; this is usually declared in the fine print for your Milestone 1 position or Intellectual Property student deed poll which either the university or the external will want you to sign. Once you have signed that document the default position most likely is that the external company owns all the IP. You may have partial ownership or some sort of inventor rights but, at this point, your IP "default position" is more akin to that of an employee (i.e. where the paying employer owns all IP) than a student despite the substantial pay difference.
(My experience here is as an Australian PhD student here who paid $X,XXXs for an IP lawyer after my external company gave me quite a colourful IP deed poll to sign which needed some amending...)
As a bonus tip of advice, make sure to READ the IP deed poll (most academics, staff and students very foolishly don't and sign away a LOT of their own power and hard work). Check also for clauses on Background IP, as you may not even be allowed to sign background IP which you're claiming is yours but legally isn't (i.e. if you've come from another university or company and are using their IP).
Contact the specific University office of commercialization (or whatever name it goes under, sometimes paired with business, sometimes paired with research etc...). They will tell you the explicit rules.
A quick google comes up with:
https://www.monash.edu/monash-innovation/about/our-people/commercialisation
I have recently had to consider similar issues as well in regards to a top up scholarships related to a CRC.
The IP agreements for CRC's often have a clause similar to this:
Subject to clause x all Intellectual Property developed as a result of the conduct of the Project is owned by the CRC.
Such IP clause are highly burdensome on the student. A PhD is a period of 3 years of research where you the student are relatively likely to discover something of potential value compared to other periods in your life. So many students end up forfeiting the opportunity to own IP of value for something in the range of ~45k if getting a top up (~15k x 3 years), or 105K for a PhD scholarship (~35K x 3 years).
Just to clarify how bad of a deal this is, a full AGRTP scholarship of ~35k per year is already quite low (in my opinion) for the work done by a PhD student, but you the student own the IP. Now consider the CRC version were you get the same very low wage for the work done but on top of that you lose the ownership of IP, one of the potential options for a career path and significant financial upside from a PhD, and you have quite a terrible deal.
For some students with absolutely no ambition of entrepreneurship it might be ok. But often I don't think students know where they want to go after their PhD and don't quite understand the IP agreements and requirements so they end up losing a significant pathway available, before they know it.
On a societal level I actually think it is quite tragic, as Australia would be well served to have more PhD students trying to turn their research into startups.