Currently, 90% of Australia's land is inhospitable desert. What geographic changes need to occur for its southern side to become fertile soil?
When you state "its southern side to become fertile soil" do you mean the southern coastal region or the southern half of the continent from the center of Australia to the coasts?
Either way getting fertile soils in most of Australia is difficult.
To begin with, the landmass of Australia is old and it has changed little in millions of years. Except for the east coast, and in more recent times (some 5000 years ago), it has had little volcanic activity. Volcanic activity can result in soil fertility.
Being so old and weather affected, Australia is the most weathered land mass on Earth. Much of what is referred to as soil in Australia would be called sub soil elsewhere. A lot of soil has just blown away over time.
The photograph below was taken in the 1930s. It shows two women standing next to an exposed tree root, from a tree that has long since died. What the photograph shows is the depth of soil erosion (approximately 2 m) that has occurred in that part of the country since European settlement, less than 200 years.
Over millions of years of weathering with no new additional soil from volcanic activity of erosion of mountains Australian soils have been leached of minerals and nutrients that most plants require. Most Australian soils are severely lacking in phosphorus and trace elements.
Despite all of this, Australian agriculture is successful because of the use of fertilizers designed for local soils in the regions.
In the central part of the south coast of Australia is the Nullarbor Plain. It is a vast region of limestone country (200,000 square kilometers), with very little soil.
If you want natural soil fertility in southern Australia you will need a mountain building region and possibly some volcanic activity. A wetter climate would also be required as well as an accumulation of soil humus.