I eat much less calories than I used to. Around 1100-1200 C. Will I lose weight if I don't exercise daily? I do exercise but only once/twice a week.

That will lose U- -weight but without exercise U will metabolize muscle also. With exercise U can prevent it. An exercise program should B 3X/week. Best is weight training 1 day @ a day of rest which should B cardio. Also U need 2keep Ur protein intake above 50gms/day. So supplements may B needed on heavy days. If U do U must include this in Ur caloric intake. U maybe should boost up the calories if U do this.
Less calories. can be helpful w/weight loss but you will plateau at some point, perhaps before you have reached your goal. Please see your doctor for a safe and healthy diet. Low carb and higher protein diet can work well for some folks rather than counting calories. Consider exercising on alternate days. Peace and good health.