As far as I know (from listening in karate class) martial arts started in China and were brought to Japan along with calligraphy and art. However, the stereotypical, "karate" (there are many many different forms) was "invented" in Japan.
Karate was created in Okinawa. It was brought to Australia by the Japanese and Okinawans. While there were certainly practitioners there a long time ago, it was probably in the 1930's that it was first brought to the country.