Upon choosing the broker offering the desired products, one can usually discover the requisite steps for account opening via the broker website.
For binary options, there probably aren't that many in Australia to choose from.
In years gone by, I've traded with a few brokers that did offer binary options (or similar), namely IG markets, and CMC markets, both of whom have an Australian presence.
On the subject of alternatives to binary options, depending upon one's trading style, CFDs (Contracts For Difference), or ETOs (Exchange Traded Options) might be worthy of some consideration.
Although they don't offer binary options, Plus500 might also be worth some consideration.(I mention this broker due to having had mostly positive experiences since I commenced trading their products.)