The majority of Australians want a republic. There is also strong support for a change of flag (though I don't know if it's reached a majority yet). We had a referendum on the republic in 1999, but the question was cleverly worded in such a way as to divide the republican vote, since it did not merely ask "Do you want Australia to become a republic", but required consent to a specific form of republic which is not universally supported amongst republicans. Consequently, many republicans voted against it (along with the monarchists) and the amendment did not pass.
Our Prime Minister at the time was the strongly conservative John Howard (Liberal Party; our equivalent of your Tories), who is openly monarchist and was keen to stifle the republican debate (which he successfully achieved via the skewed referendum). Our current PM is the less conservative Kevin Rudd (Labour Party), who has promised to make Australia a republic. The change is inevitable; it's only a matter of time.
Despite this, many Australians (including some republicans) would prefer to wait until QEII has died or abdicated before changing our system of government. She still enjoys tremendous respect in Australia amongst monarchists and republicans alike.
My own views have changed radically during the past 6 years. When I came to the UK in 2004, I was a strong monarchist with no desire to remove the monarchy or change the Australian flag. I am now a strong republican with a keen desire to remove the monarchy and change the Australian flag, which is an excellent flag in its own right, but irredeemably anachronistic and wholly unsuited to an Australian republic.
This political shift has been largely motivated by my realisation that the Queen is little more than a token figurehead in her own country, and is therefore completely redundant in mine. I also believe it is time for Australia to assert her own identity, acknowledging and respecting her British roots but moving beyond them to a truly independent future as a successful multicultural nation.