When travelling to/from Australia without flying, the most difficult part of the journey is between Singapore/Indonesia and Australia. For this leg, you need to find a cruise ship, passenger-carrying freighter or yacht that is willing to carry you.
One company that specialises in passenger freighter trips, Globoship, does offer a regular service between Singapore and Melbourne, which takes about two weeks, with prices starting from £1300 for a single ticket.
There are only two fare-paying passenger cabins onboard, but these are quite spacious, with full use of a small swimming pool/sauna, en-suite shower-room/toilets and medical facilities. While the cabins aren't the height of luxury, they are perfectly comfortable for your two week journey. Each room contains a double bed, sofa, sitting area, coffee table, fridge, TV (although you are only likely to have reception near the coast) and radio.
Passengers eat all their meals in the officer's mess, and a small gym is available for passengers' use.