See Gulf Times page 3, today Thursday 29 June. Basically, the story says there's a fine library here, but Qataris aren't interested, and westerners can't get past the bureaucracy.
Sorry, I don't know how to create hyperlinks here but you can get it on the web at http://www.gulf-times.com/site/topics/article.asp?cu_no=2&item_no=94713&...

The library itself is just off Ras Abu Aboud on the R/A with Jabr Bin Mohammed Street. ie, the R/a after Travel Agents R/A (Ric's Country Kitchen and Sana), heading towards Grand Hamad.
Maybe I'll check it out and report back.