Hey, Al Sadd is quite close to the shops, it's nice but the traffic will drive u crazy, as for the apartment, Al Sadd is one of the more expensive areas, u should try Abu Hamour or Bin Mahmoud, you can wear anything Decent, long pants and T Shirts, if u don't no one will tell u anything, they'll just give u weird looks and some men may try to follow u home, so just stick with the Pants and TShirt. It's not safe for a woman to walk alone. Especially if you're walking somewhere dark, as is in every country.
Other than that WELCOME 2 DOHA