mallethead: First of all, I liked the name you have chosen to post your query. It's a good one!
Second, in your query you have not clarified certain things. Are you working directly under the US government and get paid them? In this case, I don't think you may be entitled to End of Service Benefits (ESB) as per local labor laws. You may or may not get paid according to US laws and your terms of employment with the US government. However, on the other hand, if you were hired by a Qatari company such as a manpower supplier, have a legalized contract from them and were paid by them, then you will be entitled to ESB as per local labor laws.