a bad day for getting answers as everyone is starting their weekend.
Sorry but I can't help you a lot personally as I am not in Qatar.
Driving I think you will find essential but it can be horrendous now (I understand) but other women do it so go for it. It will give you lots more freedom.
Accommodation varies, there is good and bad as everywhere.
Shopping is a lot better than it was as there is now more than one large store..... a lot more.
Drinking. Alcohol is now available in many hotels, I leave it to others for the details.
At least this will get it back on the page for anyone getting in late and logging on.