If you are interested to invest in the economy of this country. There are easy ways: the most simple way if to purchase the following ETF listed at the New York Stock Exchange with your local broker:
It is basically a fund that tracks the index of the local Australian index, so you get an exposure to all the major Australian companies with a very limited investment.
Otherwise, it is not very difficult to open a local account with an Australian broker. Check here for the list of our preferred online brokers.