How to search for award space not shown on Qantas website?

I am looking for a premium eco / business classic rewards flight to London and return from Barcelona to Sydney.
Best way to search most value for points to Europe with min tax. Thanks

On the Qantas frequent flyer site.

You can also sign up for the BA executive club (UK address required for free access) to search their site as they sometimes show additional Oneworld options that don’t show up on the Qantas site.

In both cases they will only show you where there is rewards availability in a class on a flight option. If there are no or few options to choose from it is because there is no or little availability on your chosen dates.

Last chance saloon - ring Qantas, there may be some availability on airlines which they don’t show on their website. You’ll pay an additional booking fee via this method I believe.

Taxes are much of a muchness across most airlines but BA tend to have a higher fuel surcharge.