I was planning to go with my friend next spring....
I'm sorry, I should have been clearer... I'm from New York and I was talking about our spring which is around March-May.
As with most countries, the cheapest time for international travel tends to be "off peak"; which would be predominantly June & July (ie Australia's winter). However, Australia's domestic airfares tend not to fluctuate seasonally. So getting cheap "internal" airfares (say from Sydney to Melbourne) depends on whether there is a sale on or not; and not whether it's summer or winter here.
If you are travelling to Australia during the "shoulder" period (ie the northern hemisphere's spring/our autumn), the airfares should be cheaper than (say) around Christmas/New Year (when airfares are at their most expensive... everywhere).
But don't be disuaded by the time of the year. Winter in Australia (for the most part) tends to be pretty mild (by comparison to winter in northern Europe for instance). I'd suggest you avoid our spring though (ie late-September through early-November). The weather tends to be pretty erratic that time of the year. You may be lucky and strike brilliant weather; but more likely than not it will be blowy, wet, and miserable.
Hope you have a wonderful time in the land downunder.
Autumn here, I would wait until our spring months. Around October November would be great as its getting warmer but not 42 degrees warm.