Australia is a commonwealth country with a constitutional monarchy based on the “Queen of England” who is represented by a Governor General in Australia, who is appointed by the Australian Government.
Government is formed by the party that has the most seats in the lower house, - there are 150 seats, you need to control 76 seats to have a working majority. The leader of that party becomes the Prime Minister, other members of the party form a cabinet under the PM to hold Ministries such as Treasurer, Foreign Affairs, Defence etc.
There is no title or role in Australia relating to “President of Australia”
