I know some people are enthusiastic about a QR hookup, though I remember some time ago that the QR CEO was recently the butt of many jokes. Some likened it to the Middle East equivalent of Michael O'Leary.
All aside, of course moving HQ to a Gulf state would easily solve all union problems. Probably wouldn't be an Australian airline any more, though, would it? Then, of course, you'd get all the off-shoring brouhaha via the Australian public (blindly or hypocritically patriotic), the Australian media (extremely hypocritically patriotic) and the government (uncharacteristically interfering again). In other words, nice idea but probably won't work.
Saying that, no one will not fly EK because the UAE may not have as favourable democratic work rights as in Australia, much the same as no one will not fly any non-Australian carrier because of any political or social transgressions in the said home nations (let alone that some of the staff on such airlines are being paid less than their Australian counterparts).