I agree that 1200 calories is low, but the 20 points that Weight Watchers gives a 5'2" person weighing under 150 is about 1100 calories.
I am 5'2" tall, and although I do more than an hour of cardio a day, I need to cut down to around 1300 calories to lose weight. My basal metabolism is about that, and I did a calculation that, in order to maintain my weight with my current activity level, I can eat 1900 calories.
So shorter people usually have to go on lower calorie plans in order to lose anything, unforunately. I try to eat a great deal of fresh fruits and veggies, skim milk, whole grains, and lean protein like chicken and fish.
At about the third week, WW gives you a daily allotment for your exercise, but, if you keep pouring points on, weight loss also slows down to not even a pound a week.