I heard that they are dioecious. Experience seems to confirm this: 2 years of one tree flowering without setting fruit.
sigh
There are three types of Davidson's plums; D. Jerseyana, D. Johnsonii, and D. Pruriens, which is probably the one you have as it is the most common.
I have personally seen gigantic and isolated specimens in rainforest clearings with bumper crops. If yours isn't fruiting by itself, it probably just means it hasn't reached the point hormonally that it will hold on to fruit as opposed to abort them. It's probably too young. Perhaps you might benefit from holding off on making premature assumptions based on facile observations.
http://www.anfil.org.au/key-native-species/flavour-of-the-month-april/Here's a picture of a Davidson's Posted by a fellow Aussie on the Daleys site last year, which shows exactly what I am talking about.
As for the fruit, again, it is extremely sour. It is not eaten fresh out of hand, unless you happen to be a cassowary. It is used to make jams, and one Australian company has begun using it to flavour yoghurt. I am sure it has other applications I'm not aware of. Probably it is used to make wine also.