Ask other Jewish people and don't trust random strangers that are not Jewish. You are playing with fire here, since there is a not-so-remote possibility you will be detained as an 'Israeli spy' in a dictatorship with no human rights culture.
Qatar funds Hamas and does not recognize Israel. If you have Israeli citizenship you could be in trouble, if you visited Israel or know Israeli people you could also land in trouble.
How would they know? That's a function of how Jewish is your name and how much work they (or their intelligence) will do on your name, looking it up on Facebook, checking it against leaked lists of Israeli citizens and so on.
I don't want to scare you so I'll say that the probability that something bad could happen to you is very low. But it is there. And if something happens you will be in a dictatorial country at the mercy of their government.
To minimize your chances of trouble I'd suggest you speak with people in the Jewish community who know people who went to Qatar or to other Arab countries and keep a very low profile there.