Last year I stayed at Fitzwilliam College, Cambridge University (UK), while attending a conference. The booking was through "http://www.universityrooms.com/en/". They just sent a message to say they are also offering rooms at Australian universities. It would not be quite the same as an OxBridge college, but a night at a university provides a change from the typical hotel room.
In Canberra, there are rooms at University of Canberra, in Sydney at Sancta Sophia College and Melbourne Graduate House.