General rule of thumb in Qatar is not to listen to what people on QL advise you to do. So don't listen to what Gypsy says and don't listen to what the others say.
So the conclusion is:
Do not wear Abaya to beaches
Do not wear T-shirt and shorts.
Do not wear Bikini.
So I would advise you to go naked!
But follow the thumbrule and do not listen to me too!