Not my daughters, but I've had two friends with eating disorders.
One of my really good friends is battling bulimia and anorexia currently. She's really come a long way after she started seeing a therapist who specialized in eating disorders/PTSD. She also has a very strong support system of friends, but the first step she did was going to a therapist.
She wasn't to the point where her BMI was dangerously low, so a medical doctor wouldn't have helped. She had a normal BMI but would throw up after eating, take diet pills or laxatives, etc. But the reasons she turned to eating disorders were rooted in childhood trauma, insecurity about school/grades, and anxiety/depression. Basically, it was her way to control things when things in her life seemed out of control. So therapy really helps her address the root causes of her eating disorders and her support system helps keep her on track (ensuring she knows there are people she can call whenever she's considering diet pills, people who keep her accountable and make sure she eats, etc.).
Unfortunately, this is not my first friend to battle eating disorders. My other friend (also had both bulimia and anorexia) is trying to beat both disorders without therapy (she was too afraid to ask her parents for help). Her disorders were caused by insecurities with her looks. She didn't fit in with the crowd she wanted to be in during high school, which drove her to both bulimia and anorexia. Those issues continued into college and every time she had issues in her sorority or a guy dumped or used her, she'd turn to her eating disorders for control.
I'm not a medical doctor or psychologist, but in both cases there were root causes that needed to be addressed and the eating disorders were used as a means of control.
Based on the fact her BMI is low, I second the idea of taking her to a medical doctor. Maybe let them know you have suspicions and see if they can talk to her. Both my friends were reluctant to tell their parents fearing that they would seem weak or something like that. Both of them opened up to friends. So maybe if your daughter is having issues she will open up to a medical doctor. If you're still concerned after the visit with the doctor, I'd look around for clinics or therapists that specialize in eating disorders. Ultimately, the root causes of the eating disorder must be addressed for it to go away and that will take time, support, and possibly therapy.