My fiancé and I are both deployed. He is in Iraq and I am in Qatar. There is a four day window in which he will be able to fly in and come see me. I want to know what legal paperwork I would need to prepare ahead of time If we got married here. Is this even possible?

I don't think we are going to do it here but I would like to know our options

This scenario is different... you both have to contact your supervisors.
The Army, Marine, Air Force, have administrative office that handle all paperworks for the whole unit. This will be very easy...

Congratulation!

Ok, you are both in the military, So you have to get OK from both of your departments for the marriage, and you will need to get with the legal department and/or the chaplin as to what marriage license you will have to use or get there.