Why yes indeed! You need to eat more to lose weight. You should consider 1200 calories to be the bottom line, generally.
And, the additional calories shouldn't be birthday cake...
Add protein--from reading lots of threads, I've noticed that when people aren't eating enough calories, they are also cutting protein too much. Think of--eggs for breakfast. cheese in measured amounts (say, 1 oz. per meal or snack). lean meats. chicken, turkey. fish! tuna packed in water and fresh tuna are really almost pure protein. measured amounts of nuts and nut butter. You get the idea!
Hang in there!
Jay