Travelling to Australia without flying is difficult, expensive, time-consuming, but also one of the most rewarding overland trips imaginable. The total journey time is something like five weeks in total, and in that time you will sit on numerous trains as well as ships. There are a few different ways that this trip can be made, but the quickest utilises the Trans-Siberian Railway as a tool for crossing continental Asia.
Singapore / Indonesia - Australia
The most difficult part of this journey is the leg between Indonesia/Singapore and Australia. The problem is, that there aren't too many good options for travelling between the countries without flying. In fact, there are only three real ways to do it, and that is by cruise liner, cargo ship or on-board a private yacht. If you wish to try any of these options, read the details found in the route details below for more detailed information.
If you are feeling adventurous, you could head to the harbour and ask around to see if anyone is in a position to carry you on their boat. Darwin in Australia is known to be a good spot to try, as many boats heading our from Australia stop here en route.