My approach would be…
- Narrow down the entry and departure airports you’d be willing to fly to, across the Qantas, Emirates and oneworld network, and list these out
- Do the same with your dates - what’s the absolute earliest and latest you’d be willing to depart and then come home
- Note down the main hubs you’ll be travelling through in case you’ll need to stopover - for example Hong Kong for Cathay, Dubai for Qantas/Emirates, and potentially Singapore or other asian ports if you end up connecting a Qantas and BA flight, or Doha for Qatar Airways (there are more options here, these are some of the main ideas that crop up)
Start by then searching for ‘direct’ flights between Sydney and Europe according to your dates and preferred airports. By direct I mean one stop, but with no stopover, so you are just using the Qantas.com and/or British Airways search tools to search Sydney to Europe and seeing what options come up, if any. Be methodical, work your way through all cities and date possibilities.
Then if you can’t find anything with no stopover, start searching from Australia -> Hub city, and then Hub city -> Europe.
Finally, if you still can’t find anything (or if this sounds like a horrific use of your time) then consider employing a professional points redemption service at a cost of about $200 USD for the first passenger and $100 USD for each one after.