the Doctor has visited Australia many times. For example, the 10th Doctor and Martha discussed the Sydney Opera House, the 5th Doctor talked about playing cricket in New South Wales in Four to Doomsday, and the 4th Doctor mentioned meeting Dame Nellie Melba in Melbourne in The Power of Kroll. He also visited Australia various times in the comics, audios, and novels. He even had an Australian companion (Tegan), whose accent was nowhere near as atrocious as his American companion (Peri).
We've even seen him in Australia a few times on-screen, such as when the 11th Doctor took Kazran and Abigail to the Sydney Opera House and Uluru/Ayers Rock in A Christmas Carol.
But if you're looking for a more extended on-screen stay, there has only been one, and it was a very, very long time ago. The story was The Enemy of the World, aired (in the UK) in December 1967 and January 1968.
We don't make the show, so we're not the ones you need to whinge to -- at least, not if you want to have a chance of getting something done about it. Try the BBC. They're the ones who do make the show.
Then again, we all know that Australia is going to be vaporised by the Daleks in 200100 (The Parting of the Ways), so maybe they just don't want us to get too attached to it.