Australia

Australia is both a continent and a nation located on Earth.

History
Circa 40,000 BC, five Euterpians stranded on Earth visited Australia and taught the Aborigines to sing. (MA: Invasion of the Cat-People)

Circa 35,500 BC, Australia was the site of Monarch's first visit to Earth. He abducted several Aborigines, including their leader Kurkutji, and gave them android bodies. He promised Kurkutji rulership of his people when Monarch made his final visit to conquer the planet. (DW: Four to Doomsday)

In 1863, the Doctor dropped off Charlie Fisher in Australia to give him a new life. (TVC: Backtime)

In the 1920s, the Doctor met Australian opera singer Dame Nellie Melba and learned her party trick of shattering glass with a high-pitched note. (DW: The Power of Kroll)

In 1932, the Doctor met Australian cricket champion Donald Bradman and took five wickets for New South Wales. (DW: Four to Doomsday)

In the 1970s, the Doctor, in an attempt to escape his exile, got his TARDIS to materialise in the Australian desert, where, with the aid of Murray Stevens and some Aborigines, he defeated Rudolph Steiner's plans. (TVC: Gemini Plan)

Some time later, a group of Daleks based underneath Antarctica used a captured naval submarine to attack Sydney. Their plan to use the city as a base from which to convert Humans into slaves and conquer Earth was defeated by the Doctor with the aid of Lt. Davis. (TVC: *Sub Zero)

Some time later, the Doctor and Sir Humphrey Picton visited an Australian radio telescope base to observe the test run of Dr. Louis French's new radio wave accelerator. The Doctor realized that its use would cause disaster, and tried in vain to prevent it. The accelerated radio waves disrupted Earth's atmosphere, creating a huge storm that heavily damaged the research station and resulted in French's death. (TVC: Is Anyone There?)

In 1979, the Doctor saved a man in the Australian desert from being killed by a piece of Skylab by advising him to take three steps to the left. (DWM: Three Steps to the Left)

On 14th July 1993, the Doctor met with 37-year-old Dorothée in a café in Glebe. (NA: Set Piece)

In 1995, the Doctor, Ace and Bernice Summerfield visited the interdimensional café in Glebe. (NA: Set Piece)

In 1996, the Doctor, Chris Cwej and Roz Forrester visited Sydney for a week. (NA: Return of the Living Dad)

In 2017, the Doctor and his companions Jamie McCrimmon and Victoria Waterfield arrived on an Australian beach, where they soon became embroiled in the machinations of Ramón Salamander. (DW: The Enemy of the World)

In the 51st century, Magnus Greel was ruler of Australia. (DW: The Talons of Weng-Chiang)

In 200,100, Australia and its neighbors collectively formed Australasia. This area was depopulated by the Daleks when they attacked Earth. Whether the Bad Wolf entity restored the population of Australasia and the rest of Earth to life, as it did to Jack Harkness, is not currently known. (DW: The Parting of the Ways)

Other facts
One of the Doctor's later companions, Tegan Jovanka, was a native of Australia, having grown up on her father's farm near Brisbane. Her Aunt Vanessa was also from Australia. (DW: Logopolis)

The Doctor bought a beach-house in Sydney while his house in Kent was being painted. (NA: Sleepy)

Cities

 * Brisbane
 * Melbourne
 * Sydney