Hello Arnoy,
I happy to note your post is written in near-perfect English which I don't get to read so often at Qatar Living.
I am using the term "near-perfect" as the word "guys" that you have used in your post, does not exist in the English vocabulary. The word is absolutely American. In British English, the word "guy" refers to a figure of Guy Fawkes burnt on Guy Fawkes Night.
Now coming to your desire of teaching the English language in Qatar, I believe you stand a good chance of finding a teaching job here. In Qatar people believe and believe very firmly, that it is only the "native speakers" of English who really know the language. And they are willing to pay through the nose to get hold of such "native speakers." It is something I firmly believe to be nothing but just hogwash. Added to your qualifications and experience is that you possibly hold a western passport. In the Middle East and that applies to Qatar as well, if you hold a western passport, all the stars in the sky will shine upon you.
As such, give it a try by applying to various schools and educational institutions here, and let the heavenly stars do the rest of the work!
PS: I am not a native speaker of the English language.