Hi lbab, sorry your dd has made herself sick. That is our worst nightmare as parents I think. However, it's great that she was not secretive about it and that she agreed to go to a GP with you. A very good sign I would say. You must be a really good listener.
My younger teenage dd also has a much more solid body than her best friends who all seem to be very willowy (not all of them are I'm sure but it just seems that way to dd). She is just starting to talk about her own body negatively. I was a similar solid build but not overweight at that age. I never minded but I think the fashions were more forgiving then and we didn't spend so much time looking at photos of ourselves.
I point out women like Beyonce or Scarlett Moffatt to her . Women who are gorgeous but not super slender. She pretends not to be interested but it must go in.
Counselling would be a good idea but I think you should also firmly tell your dd that she is fit and beautiful as she is. She may not agree immediately but it will sink in.
I bet your daughter is lovely. Tell your daughter that she does not need to lose weight. Tell her she is beautiful enough as she is. If she is fit and healthy and she is not happy about the way she looks, then its just her clothes that need changing.
I am thinking of treating my dd to a personal shopping session at Topshop soon to help her find a great look for her shape. I've got a feeling they will be lovely and complimentary and it will give her a real ego boost. Could you do something like this? It can really help to have someone more knowledgeable show you which jeans will make you look better. Much healthier than going shopping for skinny jeans with much slimmer friends!! If you can afford it and you know the right shops to go to where the assistants are tactful, you could also take your dd to get a bra fitted, a swimsuit fitted etc etc - like the people over on the Style and Beauty thread do. That will make her feel gorgeous.
Sorry this post is so long. I feel very strongly about this subject!!!
In fact I have a long rant which my dd sometimes has to endure which points out that most real life women who are really at the top of their game in politics / business / singing / journalism /comedy / writing /architecture /acting /cooking / science / poker / police / etc etc etc are rarely skinny like models (or the actors who play these real life women in films) - because unless you are naturally really slim being skinny is actually a full time job. Imagine if all those women had concentrated on being skinny and obsessing about food instead of getting on with their lives. The only reason to be super slim is if you want to be a fashion model or an American actress or you live in a house with a very narrow door.
You are a lovely mum. Hope your dd feels better about herself soon. It's a mad world.