If I go on the 1200 calorie diet do I have to exercise?

I'm 16, 5'3, and weigh 153 pounds. My goal weight is 120. I've been on the 1200 calorie diet for about a week now, I eat pretty much the same things as I had been just not as many snacks because i don't have the room for it in the diet. I normally eat some cereal for breakfast, sometimes dry (200) other times with milk (around 300), for lunch I eat whatever is available but I rarely go over 300 calories, for dinner I eat around 400-500 calories. After that I normally eat a powdered donut or two if I can afford it. I sleep a lot and spend my time watching tv. I read that if you multiply your current weight by 12 and subtract 1,000 that's the number of calories I need to eat to lose weight fast. But that number comes out in the 800s and I also read that eating less than 1200 calories a day is unhealthy. I want to be 120 by the time I go back to school in August.