Know that 3500 calories = 1 pound. You say your BMR is 1427 and you're eating 1200 cals max, that makes a loss of 227 calories daily through food. Now you want to be exercising as well and you say this is ~150 cals burned.. add that to the total calories lost in a day and that's roughly 377. If you exercise every day and keep up with the eating, you'll be losing 2639 calories a week; 861 calories short of losing a pound every week.
Definitely do NOT cut back on your calories. 1200 is very little, especially when you're exercising and damaging muscle (get a lot of protein in there!). If you'd like to lose more, concentrate on working out a little harder or longer (or both!) If this still isn't for you, then reevaluate things: maybe try losing a little less per week?
Don't rush your body so much if it isn't able to handle it. Go at a slow but steady pace, usually this works for people instead of trying to meet this deadline in their head where they get discouraged so fast and give up. Being healthy isn't a short-term thing it's a lifestyle and losing even just a pound a week is great!
Also, please remember to eat very little but VERY often. I cannot tell you how horrible it is to have to go hungry for a few hours, whereas if you're constantly eating ~100-200 cal snacks, you feel full all day.
