From the Bureau of Meteorology

The aurora australis is sometimes seen in the night sky over southern Australia - mainly in winter. It usually appears as a bright arch. Streamers of light frequently radiate from the arch and sometimes extend beyond the zenith. Occasionally the arch resembles a swaying curtain. The aurora is an electrical phenomenon usually associated with magnetic storms.

From the Astronomical Society of Tasmania

Occurrence of the Aurora over Tasmania
Due to its proximity to the general location of the auroral oval, Tasmania is the likeliest of all Australian states to see auroral displays. The Australian Antarctic Division in Kingston has calculated that the chance of observing an aurora in Tasmania, on any clear night, averages out at around 1% to 2%. Because we are equatorwards of the auroral oval, auroral displays in Tasmania are generally seen in the southern sky, although under very active (storm) conditions the auroral oval expands over the state and displays can occasionally be seen to the north. Compared with other locations at our geographic latitude, Tasmania (especially Hobart) is particularly favoured to see the aurora because the invariant pole is pushed in our direction every night.
At Tasmania's latitude, the aurora usually has an angular extent along the horizon of 50 to 100 degrees and usually reaches no further northwards than the zenith (the point directly above the observer). Displays tend to be centred on the magnetic pole, which is about 19o to the west of the geographic pole. Only on rare occasions does the aurora cover the entire sky.