I'm a bronze and echo the difficulty of doing this, but it is possible. I wanted to get business seats (which I managed) but Economy or even PE should be a lot easier. I'm not sure what class you were trying for. My comment below is mostly based on my experiences finding business tickets to Europe.
Firstly forget about travelling on Qantas itself on one of flagship direct Australia-Europe routes, they make pretty much nothing available.
You're going to have to try partner airlines and unusual routes using the Qantas multi-city tool. I haven't checked your dates but when I was doing this a while ago I found:
- JAL had pretty decent availability (They fly to London, Frankfurt, Paris and I think a couple other European stops. This is how I booked Sydney to London for March next year). At the time Japan was closed so I don't know if availability is no longer easy for JAL.
- It seemed pretty easy to get Malaysian air tickets from Australia to Kuala Lumpur on business
- It seemed pretty easy to get Qantas tickets from Australia to Jakarta on business
- It seemed pretty easy to get Qantas tickets from Australia to Bengaluru on business, and then find availability on other airlines to BLR to to Europe (e.g. BA). You might need an Indian Visa if you do this but an overnight in India could be an interesting option.
- Finn Air had a few routes from Asia to Helsinki which had fair availability.
Qatar and Qantas hate each other's guts now so availability is limited, and Emirates has insane carrier charges to the point where it's not worth it, so you're unlikely to get there through the Arabian gulf.
The flightconnections.com website is really handy. Check flight maps for JAL, Finn Air, BA, Malaysian as your main ones. Cathay Pacific seems to be starting to come back online now too. Qantas also partners with Air France and KLM but availability also seems pretty limited to Asia whenever I check. Theoretically you might also be able to get something with Royal Jordanian or El Al (Israeli) but I haven't tried those routes from Asia to Europe, similar with Sri Lankan Air.
Depending on how much you value your time, when looking for my dates I was even able to scratch together a whacky SYD-KUL, KUL-HKT, HKT-HEL, HEL-LHR option.
Using the points is definitely not as easy as earning the points!