Oh, Beela, I don't think you will experience discrimination personally. Like you, I am surprised at the ethnicity question by your prospective employer but some things are different here. I'm afraid that a lot of the discrimination in the Gulf is socio-economic. Sad to say, if you dress and speak as an educated, prosperous person you won't encounter blatant racism in Doha. And if you do, just deck 'em.
Mandi