Qatar has many trade projects with Israel,even though not declared but yet they exist.
But still the people are a kinda sensitive to dealing with Jews due to being unable to destinguish between Jewdism and Zionism.Unfortunately Israel has managed to make relate zionism to the Jewdism which is untrue.
Anyways,you will find many difficulties trying to reveal this fact especially in social gatherings but with your good attitude and well behaviours I am sure you will be able to get along well.
Good luck to you and your wife.