Australia still currently recognizes itself as a commonwealth country, making this question extremely difficult to answer. The first government of the colonies was in 1823 but came together to create the Commonwealth of Australia in 1901. The statute of Westminster was written in 1931, and adopted in 1942 (backdated to 1939 due to WW2). The Australia act was completed in 1986. This means that Australia as a sovereign nation is as old as 83 years, or as young as 36.
Australia is a unique country with an interesting past. It is the only country in the world that is considered both a continent and a country. Human habitation of the Australian continent of its indigenous people was said to have begun as early as 65,000 years ago and was first discovered by explorers in 1606 by the Dutch. After the loss of the American colonies due to the War of Independence, the British government sent fleets of ships to establish colonial control over the continent, naming it New South Wales. The colony was initially considered a penal colony, sending prisoners from the British Empire to settle there and construct infrastructure. The rebellion of 1808 turned this into Australia - and in 1901, New South Wales was renamed the Commonwealth of Australia.
Due to its vast natural landscape and resources, the nation flourished after both world wars and is considered to be an extremely developed country. During the Afghanistan war, Australia increased trade activity with East Asia, becoming one of the few nations to have good relations with both China and the United States in the current political landscape.
The country of Australia is 123 years old, founded in the year 1901.