You should be able to file a claim with the carrier after the passage of 21 days. Under the Montreal Convention a bag is deemed lost at that point, even if it is later recovered. Under the Convention, QF's total liability is fair market value to a maximum of approximately AUD 2,200.

It is almost always easier to deal with travel insurance. You should carefully check claims deadlines as many policies have strict time deadlines and if you fail to file a claim or at least notice of a claim, you may forfeit anything later.