Well, the general rule I've enforced when it comes to the relation of military to civilians is ten percent, though this largely adheres to wartime situations.

If you want to use a base to look at for reference then there's no harm I see in at the least looking into the current state of the Royal Australian Navy and gauging what can be changed to make it more probable.

[url=https://en.wikipedia.org/wiki/Royal_Australian_Navy#Current_ships]https://en.wikipedia.org/wiki/Royal_Australian_Navy#Current_ships[/url]

At a quick look most of their own fleet is basically built pretty light. You wouldn't expect them to even survive an actual naval engagement and the bulk of what I suspect they could do is anti-piracy measures against the run of the mill Indonesian pirates. But when it comes to challenging the Chinese or Japanese fleets - as both being dominate regional powers - they really couldn't hold up. At the best maybe the Australian Navy could mount a landing if you use similar numbers, but prolonged naval engagement wouldn't be possible.

Historically I imagine this boils down to them being a part of the British Empire and the Brits themselves would have been the ones to own, operate, fuel, equip, and man the many larger flag-ship and main battleships of the Empire or Commonwealth's navy. So most Aussie craft would act in a support role in any event.

So a bunch of small and lighter class ships, or logistical things. A reconsolidation or collapse of the British military would leave Australia very much vulnerable potentially.

Consideration given to the pre-divergence structuring of the Australian navy would be most useful. From the same Wiki page (because quick reference material):

"The Commonwealth Naval Forces were established on 1 March 1901, two months after the federation of Australia, when the naval forces of the separate Australian colonies were amalgamated. A period of uncertainty followed as the policy makers sought to determine the newly established force's requirements and purpose, with the debate focusing upon whether Australia's naval force would be structured mainly for local defense or whether it would be designed to serve as a fleet unit within a larger imperial force, controlled centrally by the British Admiralty.[1] In 1908–09, the decision was made to pursue a compromise solution and Australia agreed to establish a force that would be used for local defense but which would be capable of forming a fleet unit within the imperial naval strategy, albeit without central control. As a result, the navy's force structure was set at "one battlecruiser, three light cruisers, six destroyers and three submarines"."