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Generally airlines only allow credit for trips after joining their frequent flyer program, or in some cases a month or so beforehand. So I am afraid the trip 18 months ago is far too long ago to now get credit for it. The more recent trip may or may not be able to be credited.
If you flew with Qantas I think they limit credit for flights 30 days before joining, and you will need to submit proof of flight (ie boarding pass). The Qantas website has a link where you can join Qantas Frequent Flyer (upon payment of a fee if residing in Australia or NZ).