This just-published article is a bit tangential to the original question, but might allow a decision on which airline to choose:
https://theconversation.com/major-ai...chieved-127800
Whenever I've booked a flight on Qantas I've been given the option to carbon-offset (at extra cost), and they aren't shy about promoting it:
https://www.qantas.com/ar/en/qantas-...ffsetting.html . I think that it's more than just green-washing, but it would be a research project in its own right to find out the effectiveness of this schemes.
The reality of travel to and from (and even within) Australia is that it involves plane flights because of the distances and because Australia is 'girt by sea'. Australians have an interest in ensuring the sustainability of plane travel or the country risks being isolated if the carbon impact becomes unsustainable.