Although you will lose weight if you stick to a 1200 calorie diet, it will be a much steadier and consistent loss if you do a bit of exercising too. Anytime you cut back on the amount of food you normally eat, your body starts to worry. It will even start to burn muscle tissue to make up for the loss of fuel coming in. Your metabolism will slow down and you will stop losing weight no matter how little you eat.
In order to keep your system revved up, and keep your muscles in good tone, exercise at least four times a week. Thirty minutes every day would be ideal, but it might be too much to change if you just started a 1200 calorie diet. When you exercise, it increases you metabolism, not only while being active, but for hours afterwards too. It is also an appetite suppressant so you will not want to eat as much.