Here's a link to the Commonwealth Director of Public Prosecutions prosecution policy.

Australia's CDPP says:

In a formal sense all prosecutions in the summary Courts are private prosecutions, even if the informant holds an official position.

The right of a private individual to institute a prosecution for a breach of the law has been said to be "a valuable constitutional safeguard against inertia or partiality on the part of authority" (per Lord Wilberforce in Gouriet -v- Union of Post Office Workers [1978] AC 435 at 477).

I agree with Lord Wilberforce - here's more of his and the other Lords commentary:

"Private prosecutions are a useful constitutional safeguard against capricious, corrupt or biased failure or refusal of those authorities to prosecute offenders against the criminal law."

Fits the current situation perfectly I'd say.