Please do not send your original marriage certificate.

Here is the information for the state of Texas. I have had an apostille for my marriage license from them. I think it took a week.. use your relatives or your best friend at home to do the US leg work.

You can also send the State of Texas an email and ask about the process that involves the Ministry of Foreign Affairs in Washington DC and getting it attested there. Texas State government workers are pretty nice and helpful (in my experience).

Let them get the copies from the courthouse, send off for the apostille and do all the mailing back and forth in the US and then send the final documents to you in Qatar. (at least that is what I would do).

http://www.sos.state.tx.us/authinfo.shtml

Lawyers (in my humble opinion) are not needed for this.