Maybe it's because I went to an all girls school but I have to say I'm with the Dr on likely eating disorder from what you've said. Believe it or not 13 is about the age where I began to notice girls around me obsessing about weight. I was naturally thin but still had girlfriends dragging me on all sorts of diets, getting me to do Jane Fonda, join gyms and, more dangerously, taking diet pills (Dexatrim landed me with palpitations and a heart monitor, Dr never asked if I ever took diet pills so I never said anything it never occurred to me OTC could be bad). None of us needed any of this, I KNEW I didn't need any of this but I just went long with it because my friends would tell me, "Its what my big sister does". When the eating disorders started up I had zero understanding of any of it. For girls it is often a byproduct of Depression, which is normal because many kids this age are depressed given the weird hormonal stuff going on. Personally, I stopped eating almost altogether to try and be a size zero like my friend, but my hips wouldn't shrink so I was stuck at a bloated size 2 (or so I felt at the time). I would go days and days eating no more than a fruit salad per day and no-one around me noticed my food habits. Similarly, bulimia starts out pretty benign but as it progresses the person reaches a point when he/she can't keep food down any more. I suppose the easiest way to figure it out is to keep a close look at your DD's eating behaviors. Don't say anything, not a word or she'll be onto you and change herself, just watch for a week or so. Is she eating normally with nibbles here and there? Is she drinking huge glasses of water before meals? Does she obsess about food, what she's eating, how she looks, the size of her clothes? A person with an eating disorder will almost brag about being thin and clothes size. Does she seem to have an un-nautural vision of herself, is she overly critical of herself? If you ask her to eat does she run to the bathroom and keep the water on or flush repeatedly to muffle the sounds? Also, Bulimics tend to have bad breath from all the acid coming up into their mouths and their teeth eventually rot from it. Not exactly glamorous.... she may be too early on for these side effects but you never know.
I hope its not this but if it is try to refocus her attention on attributes not related to her looks. Even if it's not the trouble focusing on attributes not related to looks is the best way to prevent eating disorders in any kid.
I don't think any parent should ever underestimate the prevalence of eating disorders. They're like drinking in a way, almost everyone does it but some people can stop and others can't.