Great, everyone who has posted an answer is male, except for Fatimah. Well, Lizzie, here's my 2 cents. You will be subject to the laws of the country in which you reside in terms of marriage, divorce, child custody, inheritance, finance, employment, etc. You will need your husband's permission to work. Your husband has the legal right to take another wife. He would be granted custody of any children in case of a divorce dispute. He would need to have his sponsor's permission to sponsor you in Qatar, otherwise you cannot live here. He is not automatically eligible to even visit the US. Your marriage needs to be attested by the US Embassy. And that's just off the top of my head. I think you need to speak with the US Department of State and a good international lawyer. You're absolutely right to do your homework. This isn't about love or religion, it's all about the laws of the country in which you live.
Mandi