Good luck!
I'm one of those guys that would consider joining you if one or two things were different. In my case it is only 4 months military (bad ankle, discharged after basic), no clearance, 50-60 extra pounds, and my religion isn't exactly popular over there.
Anyway, I've never been there but I am interested in Qatar. From what I read it seems you are going to one of the most open and cosmopolitan of the Gulf states certainly, and possibly of all the Arab states. I don't think it should be a bad experience, and if you do it right it could be a great experience.
With a poli-sci degree and experience in the Middle East you are setting yourself up for some good job opportunities later (esp. if you already have a clearance). Be sure to learn the language as best you can, both now and once you get there.
Try not to only hang out with other Americans and other Westerners. Get to know some locals. Maybe visit a mosque now and again, one of the best ways to get strangers to open up is if you seem genuinely interested in their religion (and Arab and Islamic culture tend to be very generous in this respect- they make great hosts).
As Unlucky said, if you play this right, and come out of it with a real knowlege of the country and/or region you will be in high demand, possibly able to write your own ticket.
Also, as other's have said, you may want to consider buying a laptop either before you leave (check up on whether our appliances will work over there- most of the rest of the world uses a different system than we do, I think it is the voltage that is different) or when you get there. If you have your own computer and can sign online whenever you wish when off duty, that should do a lot to alleviate homesickness.
If you won't be able to do this, and you want some THR penpals to keep up with things in general, PM me. I'll be happy to give you my address and be one of your penpals (hmm, I wonder if I still remember how to write a "real" letter
).