I'm doing the same degree and am also planning to complete two majors - in Government and Industrial Relations. The only way I could fit the second major was to complete a second year IR subject in the 2nd semester of my first year. I was only able to do this because there is only 1 junior unit that you need to complete in IR in order to complete further senior units.
Anyway, I would probably recommend talking to the director of the degree program. You should be able to find his/her details on the Usyd website. They will be able to help you structure your degree program and may be able to figure out how you can complete both majors without doing summer school.