I managed to use a basic Silva compass (zone 1, MN marked on the capsule) without particular problems in Brazil (near Rio de Janiero, zone 3 (almost 4)) for a couple of events a few years ago. There was a noticeable dip on the needle, but the needle pivot was slack enough to accommodate it. Australia is further S (zone 5), and the zone 1 compass may not be so tolerant. My suggestion would be to go there with your usual compass and see if it still works for you, if not get another one locally (easier to get a zone 5 compass in zone 5, in any case).
My suspicion is that the less sophisticated (cheaper) compasses may suffer less noticeably out of zone, so it might be worth taking a small selection of compasses with you (if you have them).
Technical bit (for physics/geography nerds):…
The north end of the needle still points to the magnetic N pole in the S hemisphere, the difference in design of the compasses is the balance of the needle. The needles are balanced by the manufacturers to lay flat in the given zones. The earths magnetic field doesn’t lie parallel to the earths surface anywhere other than the equatorial latitudes, but runs into (or out of) the surface elsewhere. The closer to the magnetic poles you are, the steeper the angle of field lines relative to the surface. At the poles the field lines run vertically into (or out of) the ground. This angle of the field acts to tip the needle of the compass (which tries to line up parallel with the field lines at all times). The tipping force is counteracted by changing the balance point (very slightly) of the needle to make it lay flat.
