Here's a suggestion..why not rendezvous in a different country, pressumable one that is half way the two of you.
You see, Qatar is pretty restricted in some ways..you may not fully enjoy your stay even if it means being with him. I read you plan to stay in Doha for a couple of weeks if it presents as an option for you to know him better, am i correct? Well, you're just wasting your weeks coz i take it that he'll be working in that period of time. Give it a little more thought..you'll realize what I'm trying to say.

Also this way, you'll know if he's really into you, morever, that being able to meet each other was an effort by the two of you..not just you, who's the lady. You shouldnt let him take advantage of the fact that he can't enter US as easy as u can enter Qatar, and have you do all the work to make this relationship that you two have be a better meaningful one.