Take vacation, get it done at your home country , your relatives and friends will be at your support .. . . . ..
I get to read queries at QL asking for "the best" of something or some service. As in your case, you have asked for "the best eye surgeons in qatar". In order to get to know who is "the best" one would need try all of them out and then draw a conclusion. Remember, you have just "two" eyes.
Coming to your query, cataract surgery is costly in Qatar. The only two places I know of where such a surgery is carried out are Hamad Hospital and AlAhli Hospital. I believe there are no charges at Hamad Hospital but the waiting period is long. I had checked with AlAhli Hospital several years back and was told the cost of cataract surgery in one eye would be around QR13000. You can check with them on the new rates.
Needless to say, I went home and had my surgery done there at much lower costs plus getting the advantage of meeting my family members.