Without commenting on the merits of OP's case, I have simply got to correct a misunderstanding of the US legal system. Yes, the US does allow for punitive damages, but not unless you are a victim of a tort, and without damage, I can't think of a single state in the US that would allow you to bring an action here since you weren't injured. In the US, airlines as common carriers have a heightened duty of care -- so it's easier to show they were at fault if something does go wrong -- but this still doesn't get rid of the fact that you have to show that you were hurt.

This seems to be more of a contract case (as somebody has pointed out), and punitive damages simply are not allowed in contract cases. That being said, depending on the facts, there may be some argument that Quantas breached its contract, which I don't care to evaluate... but there's certainly no punitive damages for that.

For all those representing the legal system in the US to allow recovery whenever, wherever, please don't -- our legal system is actually quite reasonable in most aspects if you take the time to understand it... but understanding it usually takes 3 years of law school and several years of practice.