Well, she didn't, but the Governor-General representing her did. In 1975, the Prime Minister could not get a clear vote of confidence from Parliament, and Government had essentially ground to a halt. Next thing you know, the Governor-General representing Her Majesty in Australia dissolved Parliament and demanded fresh elections. It was probably the best decision at the time, but it shocked the hell out of the country, many people not knowing that could be done.
Of course, Australia could always reject the monarchy and remain in the Commonwealth as India and several other countries have done. I doubt it will, but it is possible.