Currently, the distance between Australia and Antarctica is a rough estimate of 4500 miles.
But if that number were cut by half, what would Australia's climate and ecology be?
As Vincent mentions, Darwin would become much like Tasmania, or even New Zealand. Most of the rest of Australia would be cold and horrible to live in however. The unlucky parts (ie: most) of Shiftstralia might have a climate similar to MacDonald Island and Heard Island, cold, wet, windy and cloudy. Tasmania would not quite be inside the Antarctic Circle, but it would be close. The climate in some areas would be like Macquarie Island as-well.
Australia would (in general) become wetter and colder, this could cause massive flooding and land erosion in some sandy and dry areas if there are no plants to anchor the soil. Many current native plants would not do very well, Banksia plants for example rely on the scorching summer and/or bushfires to release their seeds. Eucalypts also thrive due to bushfires. These species are unlikely to evolve in a manner that required bushfires or extreme heat to reproduce. Many Australian plants currently have thin (taper-like) leaves to reduce water loss, in a wetter climate this would not be an issue and plants are more likely to have broad leaves to capture sunlight. Expect forests of some kind.
Native animals would also be different, the ever lovable Koalas for example might not exist. Eucalyptus leaves are flammable (helps reproduction - see above) and Koalas supposedly like to eat them because of this. The Koalas would evolve to eat something else and might not be recognisable. Foreign/Invasive species (rabbits come to mind, also cane toads) would flourish in Australia. There would be no desert, so therefore no desert dwelling creatures such as the sand goanna and dingo would exist. Wolves (yay!) might exist however. Cold blooded creatures (like crocodiles) would be less common. The Great Barrier reef would not exist. Corals like warm waters, the new East Coast would be too cold for them.
Good news: The climate is much more like Europe, European species will probably survive better.
Bad news: Everything is still trying to kill you.
The distance between Hobart, Tasmania (43 degrees south) and Dumont D'Urville Station, Antarctica (66 degrees south) is : (66-43)*111,1 = 2555 km. That's a rough estimation of the real distance between the 2.
and from Hobart to the south pole is (90-43)*111,1 = 5222 km
And your estimation is in miles (so you must live in the USA?) 4500 * 1,6 = 7200 km. That's pretty far from my other numbers. By dividing it by 2, it's the equivalent of moving Australia almost 32 degrees south.
Hobart new location would be more or less where the Concordia station is at 75 degrees south. I don't know if this answer your question but if Antarctica is supposed to stay there, it will be very cold. Temperature would rarely go above -20 Celsius. Darwin, on the north coast, would be located where Hobart is now with a mild oceanic climate.