hi Becky, welcome to Doha. There are a couple of ladies groups which meet. The American wemons (dont know dates) group and Tuesday ladies group. First meeting for TLG of the 2012/2013 year is 11th sept at the Radisson blu (formally Ramada hotel) if you google TLG doha your find more info.
You may also find it useful to buy Time out Doha or HQ both have events and details of thing happening in Doha.