The listing of accommodation options this page only shows places close to the University, which are often booked out on a busy weekend. Melbourne has a number of events in January and February, such as Australian Open and Chinese New Year. Budget accommodation is often hard to find at these times.
Here are some good accommodation search sites that offer a range of accommodation, from backpackers to hotels:
Trying options a few kilometres out of the city increases your chances of finding something suitable. The public transport journey planner is a useful tool for navigating the public transport grid.
Airbnb is a site where you can arrange to rent a room from a local host, usually for a short time. Just make sure you are booking Melbourne, Victoria and not Melbourne, Florida!