The quick answer is yes almost certainly they will make it. However they have a huge amount of lessons to learn and by the outside world they are seen as the poor mans EK, almost following their every move.
I agree with HF that incompentent mangement is hindering that progress with stupid decisions like buying more A300's and mismatching aircraft with routes and wondering why we don't get the yield (a monkey could work that out) and again I agrre that The Bouncer is in denial.
The service on board is too regimented and lacks real character that sets it apart from others. To me QR are just a very average carrier, nothing more.
God forbid that anything happen to one of our aircraft, but that is one situation that could endanger the airline and its future. If it happened in Europe the press who will virtually close it down. This paranoid control freak has made so many enemies who will be willing to speak out and give out a lot of previously unpublished (on pprune) info that, lets face it, we all know about. We know the press looks at this anyway.
He's got to face up to the fact that many of the senior people around him are unexperienced, incompentant and start listening to real people. Then he might start to make some progress but not until he does.