Is Australia a Democracy? The short answer is, "No!" The legally constituted form of civil government in Australia is a Constitutional Monarchy. Some have even argued that Australia is a "Crowned Republic". Queen Elizabeth II is the Queen of Australia and the Queen of Queensland, by law and by popular consent - remember, at the last Referendum, the majority of people in the majority of states, with a majority of the total population over all, voted to maintain our Constitutional form.
A democracy is a form of government where rulership is by the people: 'demos' = people 'cracy' = rule = "rule by the people". For a democracy to be implemented in Australia there would need to be a rejection of our official head of state, and there would need to be provided a mechanism whereby every decision of government could be decided by all the people who are eligible to vote: perhaps a large hall could be built where the entire voting population of the country could meet every Monday night and vote on every issue of government. Such a mechanism would be essential for our form of government to be truly democratic; and such a scenario is obvioulsy ludicrous.
At best we could only implement a representative democracy. However, in such a case, to be truly democratic, we would have to implement ways in which the representatives could continually guage the wishes of those they represented in relation to every piece of legislation to be considered by the government. The representative would need to regularly hold meetings in his electorate, where everyone had a vote, or where discussion was held until consensus was reached. This also does not happen in Australia.
If true democracy is unworkable, then we need to rely on another form of government. With a monarchy, government legitimacy resides in the king - and in a Westminster system, the king is limited by Constitution and Parliament. In a Republic, government legitimacy resides in the president - and in the case of the USA, that authority is limited by Constitution and Congress. With an oligarchy government resides in a group, and with an aristocracy it resides in the best.
Australia's political woes do not come from the form of government that we have inherited. Arguably it is the best form of government that exists in the world. Our political woes reside in the guiding ethics of those who implement Her Majesty's governance. The only solution to this problem is for more good people to step up and take on the responsibility of representing the wishes of other good people to Her Majesty's Australian representative, the Governor-General.
The only thing that evil needs to succeed is for good men to do nothing. Too many good men have done nothing for so long, it now seems that our good system of government doesn't work any more. If good men were to offer themselves to serve the Monarch, who has covenanted herself at her Coronation to serve her subjects (which she has faithfully done for the entire duration of her reign), then the brilliance of our present Constitutional Monarchical system would once again be enjoyed.