I don't know about Qatar, but I can tell you that the medical services of Jordan are the best in the arab world and probably in the middle east.

I can assure you that it will cost you less than here by half.

If you can, try to organize a trip to Jordan as a tourist and stay there to get your eyes done at any medical center. It is filled with plenty of qualified surgeons and up-to-date medical centers.

If you decide on that, I can give many addresses...

Think of this as a 2nd option.

I went to many doctors here for many problems concerned with me, my wife and some of my kids and we all got advice to have surgery immediately on an urgent basis.

When I went back to Jordan, we all checked there again, and some problems were solved in the same clinics!
No surgery for any of the family members!

Be very careful, private hospitals and clinics here work as blood suckers!