Firstly, assuming that you're not married, you will need to be if you intend living together officially. Qatar and UAE have restrictions on this.
Secondly, flying is obviously something you are keen on and have spent a considerable sum of money attaining your current level. You wouldn't be doing this unless you wanted a career as a pilot, right? So, whilst your girlfriend is currently in a good job, she must also respect your own desire to pursue your dreams and ambitions and should be supportive in that. Marriage is a partnership after all. If you want to develop further, the ME is not the region with your current experience, Europe will be.
It's always difficult for others to offer advice, however, my recommendation is that you stay and build up your hours. See how you progress. This then affords you the chance to visit this region without committing. The ME is not for everyone. In two years or so, if the relationship is still strong, you can re assess. Your wife/girlfriend may not even be working in Doha then. Most high flying jobs require flexibility and possible re location. Further, whilst commuting and long distance relationship can be challenging, a few years sacrifice now could be worth the gain long term. If her job becomes that important, and you marry, you may decide a flying career is not for you. And what about kids?
Lots to think about and I'm sure others may offer a different perspective. Mine is don't come out now as getting back into the flying business will be difficult if you've been out of the game for a few years. Continuity is vital if you want to get on the ladder.
Good luck....
Harry