Cordyline australis isn't one of the easiest of Cordylines to propagate from cutting, your best chance is to do it in early spring.  Use a sharp knife to cut the shoots as close as possible to the main plant, trim the leaves back to just 2-3 emerging leaves then plant the cuttings into a good quality well draining potting mix or sharp sand.

To improve your chances of striking the cuttings, place the pot with the cuttings into a large clear plastic bag to create a mini hothouse.  Put this where it will receive good light but not direct sunlight.  Roots should develop within 2 months and you can pot them into tubs/containers or directly into the ground.