There are plenty of companies offering subscription music services in Australia, but virtually all of them ask for a monthly fee. Spotify is one of the few that offers a free ad-supported service, but you still have to pay to use it on a mobile device. Enter Guvera: free music streaming (supported by advertising) which you can access on iOS and Android devices.
We actually wrote up Guvera in its original incarnation way back in 2010 when it was an entirely web-based option. It has somewhat slipped under the radar since then, but the revamped version is a big improvement on the original, especially in offering ad-supported clients for Android and iOS. Aside from the expected platform cosmetic differences, both versions are similar: you can create your own playlists, check out featured tracks, and search for individual artists.
You can sign into Guvera using Facebook or set up an account via your email address. The site claims "millions" of tracks; my searches suggest that the range isn't as broad as Spotify and there are some problems with metadata on quite a few tracks, but there's enough there to keep your playlist ticking over for quite a while. If you want to avoid the ads, you can sign up for an $11.99 a month Platinum account. The free option will probably be enough to please casual listeners; as with any streaming service, stick to Wi-Fi to avoid excessive data charges.