Qatar National Library has a section with books in English (I'm guessing you're looking for books in English?!) You can find it by coming from the Ras Abu Aboud flyover at the beginning of the Corniche up the street with Sana clothes shop on the left and BA, KLM, airline offices on the right. Pass those and there is a R/A. Go straight ahead and the library is at the next R/A on your right.

I believe there is a library at the Doha Club but isn't that place due to be demolished?