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. (TVA: 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. (TVA: 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. (TVA: *Sub Zero)

Later still, 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. (TVA: 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) At the same time, Kathy Chambers set up her Chambers Pharmaceuticals company in Brisbane as cover for experiments with Cybermen technology. (BFA: The Gathering)

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

In 2006, Brisbane's phone network was hit by an electronic attack to cover for the creation of System. Tegan Jovanka was running a small company at the time. (BFA: The Gathering)

In 2008, UNIT Australia fought off an advance party of Ice Warriors. (DWM: The Age of Ice)

In 2009, after Earth was returned from the Medusa Cascade, Sydney was one of the cities celebrating. (DW: Journey's End)

In 2010, a Chronal wave hit Sydney as part of a major Skith assault. (DWM: The Age of Ice)

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 2040s, Ed Gold pushed for Australia to get involved in the space race. Sometime after 2044, Australia had built a space elevator off its western coast. (DW: The Waters of Mars)

In 2058, Australia would be part of the Bowie Base One mission on Mars. (DW: The Waters of Mars)

In 2096, Australia was the most stable nation on Earth after the Myloki conflict of the 2060s, due to a dispersed population and comparative wealth. (PDA: The Indestructible Man)

In the 51st century, Australia was either part of or occupied by the Supreme Alliance. Magnus Greel was the "Butcher of Brisbane" for his horrific experiments carried out there. (DW: The Talons of Weng-Chiang)

In 200,100, Australia and its neighbors collectively formed Australasia. When the Daleks attacked Earth, Australasia was referred to as "just... gone" after a bombing run. (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)

Eugene Jones planned to take Linda to Australia. (TW: Random Shoes)

Martha Jones told Plummer that she had been to Australia. (TW: Reset)

Australia became part of John Frobisher's relations with the 456. (TW: Children of Earth: Day Three)

In (likely) the 20th or 21st centuries the Doctor visited Australia with Kazran Sardick and Abigail Pettigrew, visiting Uluru and the Sydney Opera House. (DW: A Christmas Carol)

Cities

 * Brisbane
 * Melbourne
 * Sydney
 * Adelaide
 * Perth
 * Darwin
 * Hobart
 * Canberra

Behind the scenes

 * Katy Manning is a naturalised Australian citizen.
 * The spin-off, K9, is produced in Australia.
 * Australia was the only country to buy every missing episode — except, of course, "The Feast of Steven", which was never exported anywhere.