You can inquire from the Church of the Epiphany,

http://www.epiphany-qatar.org/.

We got married at this church. They will give you the documentary requirements prior to marriage (a lot of paperwork). Both of you have to undergo blood tests only in accredited hospitals. We had ours done in Al Emadi Hospital - QR1200 each.

I hope the above helps. You can send me a PM if you need more information. Best wishes:)