Granted, a lot of Percy Grainger's music is based on English folk songs, and he did eventually become an American citizen, but he is still Australia's most famous composer. "Gum-sucking" in the title of The Gumsuckers March refers to the way people in Victoria, Australia, sucked on eucalyptus leaves for refreshment in the summer.
The Gumsuckers March (sample)
The Warriors (Music for an imaginary ballet) (sample)
Peter Sculthorpe (homepage here) is another whose music has spread far beyond the shores of Australia. The Kronos Quartet commissioned his String Quartet No. 11 "
String Quartet No. 11 "
Requiem: Sanctus (sample)
Two newer composers worth watching are Elena Kats-Chernin and Nigel Westlake. Kats-Chernin was actually born in Uzbekistan, but considers Australia her adopted home. Her most popular work is the music for the ballet Wild Swans, but her some of her other work, like Clocks (on her MySpace page) and her rags, are even more interesting.
Russian Rag (sample)
Nigel Westlake began his career as a clarinetist and has written film and television scores, but his writing for percussion has made him a bit of a star among that set. His Omphalo-Centric Lecture was an instant hit (no pun intended...or is it?).
Omphalo-Centric Lecture (sample)
Piano Trio: Movement 1 (sample)