I would focus on getting points on the programs which you can use your points on those 3 airlines you would like to fly.
Qantas and Cathay are both part of the OneWorld alliance. The easiest way to get points for this alliance would be Qantas Frequent flyer given the amount of partnerships they have in Australia. You can also earn asia miles (Cathay’s program) using AMEX cards.
For Singapore Airlines, it is possible to redeem Velocity points for that and it is quite easy to earn as well with many partnerships in Australia. It is also possible to transfer Velocity points to Krisflyer at a 1.55:1 ratio if you want more access to Singapore Airlines premium cabin award space. Otherwise, Krisflyer miles can also be earned via credit cards such as AMEX, Westpac and more.