As a general rule, Tiger Airways and JetStar have the cheapest flights available. You just have to visit their respective websites and you can browse around for their fares. On the other hand, Quantas and Virgin Blue are more expensive. However, they do have some cheap flights to Australia through the deals and discounts that they hold from time to time, which you can avail of if you just check on their website.
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For air travel within Australia or traveling to and from regional destinations, you can choose among Regional Express (also known as Rex Airlines), Skywest, and Airnorth. The last two airlines have their niche in smaller cities in the Northern Territory and Western Australia. Rex has the most destinations amongst the different Australian states. It has regular flights to and from the major cities of Sydney, Melbourne, Canberra, and Adelaide as well. If you have a HI/YHA, IYTC, or ISIC VIP card, you can avail of Rex’s backpacker travel passes wherein you get to have unlimited cheap flights Australia travel on selected destinations at $499 for one month or $949 for two months.