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?
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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).