Our economy relies almost entirely upon that of China, but our media outlets don't seem to understand that; they try to antagonize the Chinese, and strain relations for the sake of ratings every five minutes.
Also, we have totally unique wildlife - a result of a roughly eighty million years of separation from any other continent, lots and lots of which is deadly. We also had the bright idea of introducing Cane Toads (highly poisonous) a while back, and now we spend tens of millions every year trying to kill them off.
Our uranium deposits are the largest in the world, but we have no commercial or military nuclear programs, and instead sell all of our uranium off.
Our prime minister is a complete idiot. No one likes her, in case you were wondering. She used to be a lawyer. /shiver
Our country is home to this chap called Paul Hogan, and thanks to him and the Simpsons, the rest of the world thinks of us as a nation of bogans (Australian hicks).
What else? What else? Oh yes, we have funny accents and people from the rest of the world get excited when we speak. We're a part of the British Commonwealth, because we haven't got around to seceding yet.
Our proudest military moment came during World War 1, when we were defeated over a long and bloody campaign. Our minds work in funny ways.