I think you're best bet is collecting Velocity, Krisflyer or Avios.
Velocity is
Virgin Australia's frequent flyer program and is the easiest currency to collect in Australia - sign up bonuses are often higher than Qantas points and there are regular bonuses and transfer bonuses throughout the year. You can redeem Velocity points for flights on Singapore Airlines, Qatar or
Etihad to Europe. Business class redemptions one way are 139,000 points + $400 for Singapore or +$800 in taxes for Qatar/
Etihad. Anecdotally Singapore Airline business class awards are not that easy to come by on Velocity points. Qatar Seats are more common.
Etihad only releases them 30 days out to Virgin so they're a real gamble.
You can also convert Velocity points to Krisflyer at a 1:1.55 ratio. Krisflyer is Singapore Airlines reward program. They have quite high availability for business class seats on Singapore Airline flights and the taxes are quite low. You're looking at $120 or so for a one way flight in business class (+130,500 KF points). There are also quite a few bank programs (including Amex and Citibank) that convert to Krisflyer, albeit at a worse conversion ratio than to Velocity.
Avios is the last one and is more difficult to obtain in Australia. Only Amex and Citibank convert to Avios. Avios is Qatars frequent flyer currency and is Qatar/Avios is the analogue to Singapore Airlines/KF. As you'd imagine the benefit is lower taxes and higher availability on Qatar flights. Taxes are still not that cheap (around $300? I'm not 100% sure) but you'll only need 90k Avios for a one way AU -> EU business class redemption.
TL;DR: Collect Velocity points and convert to Krisflyer for lower tax flights, with options to redeem on QR/EY for higher taxes as a backup. Alternatively collect Avios if you're very keen on QR metal.
