You are the same weight as I am and with working out I need to eat 1500 calories a day! I know it is against our normal thinking to think eating more equals weight loss, but it does! You will lose on the diet you are trying to implement, but you will gain it all back.
To change diet is to change the way you eat forever. There is no way you can survive on what you are trying to eat now.
Here is a day I logged and I forced myself to eat:
Breakfast:
1/2 cup plain oatmeal with cinnamon
Protein shake w/skim milk (I use water some times as well depending on caloric needs)
Snack:
3 boiled egg whites, 1 apple
Lunch:
Protein shake with frozen strawberries (I was short on time on this day)
1/2 avocado
Snack:
celery sticks with reduced fat peanut butter
Dinner:
Baked Chicken Breast 4oz
apple sauce
frozen pea vegetable stir fry
Snack:
3 boiled egg whites
Carbs: 135 (goal 188)
Protein: 113 (goal 107)
Fats: 34 (goal 33)
I was short on my calories as well

You also need to remember our metabolism is like a fire. You need to start the fire off right with a good amount of wood (breakfast) and add logs as the day goes on. Depriving yourself will only make your body retain what ever goes in. Also, you do not want to burn muscle, you want to burn fat. Not eating enough you tear down your newly built muscle.