Of course, it's entirely up to the Aussies if they don't wish to have the Queen as a symbolic head of state and leave the Commonwealth, but as a Brit who warms towards the monarchy i'll add my thoughts to this thread.
Countries like Australia, New Zealand and Canada all have a common historical heritage, they are former British settler colonies which grew into independent states. So far they have chosen to acknowledge their historical and cultural ties to Britain by remaining in the Commonwealth and having the Queen as their symbolic head of state.
The important thing here is that having the Queen as "head of state" is a purely symbolic recognition of Australia's historical ties to the UK. Like how Australia has the union flag in the top left corner of their national flag. Now, to what extent Australia wishes to display their historical legacy with the UK is entirely up to Australia. If Australia wants to drop all this symbolism then fine, nobody will stop them, i won't oppose it and the UK state certainly won't. But I think many Brit's appreciate Australia sticking with us- after all just look at the Americans.
As a final note aimed at a few misconceptions in this thread: The British monarchy has in theory powers such as the power to declare war and dissolve parliament, in reality the monarchy does not such powers, and this has been part of an unspoken status quo that's been going on between parliament and the monarchy since the restoration of the monarchy with Charles II. Britain has retained the monarchy out of tradition, and there's nothing wrong with that. Britain has a long and dramatic history that's changed the world- for the better and the worse. The monarchy's part of the British national identity, without the monarchy we'll just be another republic like most states today. But Britain's unique, we're different, we carved out the largest and last empire in history, we developed modern science and the ideas of British philosophers and writers shape the world today- the monarchy's all part of this national identity.
However, the British monarchy does actually have some power, despite me having said it actually doesn't. The British monarchy commands a lot of soft power, and by soft power I mean the ability to advance Britain's national interest through maintaining positive relations with other countries. The British monarchy, especially in republics, is heavily romanticised, the monarchy, if used correctly, can win the hearts and respect of citizens and political leaders of foreign states across the world. The monarchy essentially promotes Britain?s national reputation abroad, as the Queen has recently done in Canada and Ireland. The monarchy is a form of PR that most other nations can not possess. After all, presidents come and go, but King's and Queen's are different. Having the monarchy gives Britain an edge in conducting foreign relations that most other nations do not have.
And despite all that i've said, I should make it clear that I am no nationalist- i'm a patriot yes, but not a nationalist. There is an important difference.