My main comment was surrounding trade between the two countries which you skipped entirely. Australia gives Singapore open skies, because in return Singapore imports a megaton of fresh produce including meat and dairy from Australia. The US gets open skies, because its part of a broader strategy surrounding defence and economic ties. Same goes for China.
Yes, you put a lot emphasis on trade factor, but I don't, which is why I skipped it. I'm not so sure that aviation rights are so firmly linked to other trade, defence etc; but how 'nice' the country is to Australia generally I'm sure will come into it. 'Open Skies' is more about mutual willingness to grant reciprocity.
But if you want to look at trade and other ties between Qatar and Australia, have a look at DFAT's summary:
The State of Qatar occupies an 11,600 square kilometre peninsula on the northeast coast of the Arabian Peninsula.
www.dfat.gov.au
What are they giving us back? Competition is not a valid answer.
Why on earth not
? Cheaper anything comes with more competition. Aus-Europe is a huge (and pretty expensive) aviation market for the public and more flights will inevitably result in lower prices. In allowing more QR (or VA/QR) flights, 'Qatar' is giving the travelling public more choice and it must have an effect on cost. If QR can offer lower prices (or even similar prices with a high quality product) because of the Qatari state is behind it, as a traveller, I don't care.
Are they going to import our products? Are they going to lower tarrifs? Give us cheaper oil? Clearly Australia is valuable enough that QR wants to buy (some of) VA, so if that's the case, why can't their Gov come to the table and offer something valuable in return for flight rights?
Again, have a look at the DFAT summary above.
That said, I think the 'trade-off' you talk about here might be the significant investment in cash and IP in what has been a struggling airline. Yes, its going to Bain now, but ultimately they will be a shareholder in the listed company and a second domestic airline can only be stronger with a major global airline behind it. And before anyone says it, the previous 3-way major airline shareholder situation cannot be compared. I mean, three large competitors with influence on a small airline - what could possibly go wrong?