Originally it was to stop you from knocking your own hat off when performing "shoulder arms".
Prior to Federation, when each state had their own military forces, some had it turned up on the right, some on the left, but turning up on the left was standardised with the formation of the Commonwealth Military Forces. The turned-up side also makes a convenient spot for a corps or unit badge.
BTW it is usually called a slouch hat or, among soldiers, a "Hat KFF" (khaki, fur felt). When worn in the field the brim is normally not turned up.