Fair question. Interesting one too, I admit I hadn't thought of it so here goes.
The Governor-General of Australia (representing the Monarch) has the residual power to dismiss a government. Shocking isn't it? But it happened on 11 November 1975 (yes, Armistice Day) -
http://whitlamdismissal.com/. I'm not posting that to bombard you with info just to let you know it actually happened.
So, in the scenario, the government seeks to legislate to keep itself in power and because (let's say) it has the numbers in the lower house and also in the Senate it can pass the legislation. The legislation has no effect until it's assented to by the Governor-General. I would think that the Governor-General would consult the High Court and that the High Court would probably give it the constitutional thumbs down and advise the GG not to sign it. Therefore no legislation passed. It's entirely possible the GG would then withdraw the commission of the government, in effect dismissing it.
If the government tied to get the military involved then the GG, in place of the Monarch, would order the military not to to do so and to stay in barracks unless the GG gives orders otherwise (to the Chief of the ADF I mean).
The only police agency at the Commonwealth level in Australia is the Australian Federal Police (
http://www.afp.gov.au). They aren't powerful enough to do anything to help or hinder the government and if they did I feel the GG would get the ADF on the job which would effectively neutralise the AFP.
The upshot would be the arrest of the members of the now dismissed government. They would be tried and sentenced to prison to listen to every parliamentary speech made over the last twenty years. If that's not sufficient deterrent then nothing is.