Some people gain weight on 1000 calories/day, but very few. Your
daughter is showing the classic signs of anorexia/bulimia that is
so common among teenage girls.
You should look for a doctor specialising in eating disorders -
they know what tests to run to ensure that she doesn't have a
hormone problem. But, 99% of the time, the problem is a mixup of
self-image and self-esteem. Being a teenager is rough - I still
remember mine!
No one can be more important to her than you, her father. She
needs emotional support that she can trust, and help to build her
own feeling of self-worth amidst the mess of signals she is
getting about everything from baby Einstein to sex object.
Best of luck. And, hang in there for her.