It's the other way around though. So long as you give sufficient notice, they need to justify why you can't. In most cases unless you are literally the only person who can fulfill your role then you might have to. Basically in any situation where annual leave would have been approved, you could take unpaid leave. It is purely up to the business to justify why you can't at which case you can always challenge it and bring in a third party like fair work. Like fair work and government regulations in Australia are very employee biased. Most companies just hope their employees don't read the stuff. Like even regards to company shut-downs. If they don't provide you with written notice with enough time in advance, they legally have to pay you even if you don't take any leave (they also can't force you to take leave if they don't give you sufficient notice). There's a lot of "rules as written" stuff but honestly if you really push this kind of thing, chances are they will make your life worse and will probably breathe down your neck.

I generally advise people to read their awards and see what it covers and how you are protected. But also unless you plan on quitting, in the long run, i don't suggest you antagonise your employer.