If you are moving to Qatar either you or your spouse has been contracted by a sponsoring company. While under contract with a sponsor you cannot work for anyone else, but you may sponsor your spouse who may in turn find employment with a different company. It can be very tricky to transfer sponsorship and if you do not part on amicable terms your sponsor may chose to ban you from Qatar for two years.
It is quite normal for women, local and expat to work in Qatar. Much like everything else this can be just another part of your life in Qatar if you remember to be respectful of your host country's culture- for expat women in the workplace this can mean dressing more conservatively for example wearing a scarf with that silk camisole and men may wish to be more conscientious of physical contact such as a congratulatory pat on the back with co-workers of the opposite sex.