If you're a mum, you could join Doha Mums. It's quite an active group. You can join even if you aren't a mum (I'm not, and I just joined) but I can't yet vouch for how it will be - since most of their activities are centred around the kids.
http://www.dohamums.com/

There's also a Tuesday Ladies Group - http://www.tlgdoha.com/

I could suggest a few places where you could take yourself and a book in the meanwhile, being as I am in much the same situation for the moment :)