I agree with Neenee - she needs clinical support from a psychologist who specialises in eating disorders. You can use the "Find a Psychologist" search engine at The Australian Psychological Society (Australian Psychological Society : Find a Psychologist) . A psychiatrist would also be advised, as they can assist with hospitalisation if it is required. Be prepared to try a few out, as finding a good "fit" is really important.
Having said this, your daughter may still not want to talk to these people. Some organisations run live in or day programs for teenagers with eating disorders. I don't know where you live, but in Melbourne there is The Butterfly Foundation (run by Southern Health) and a specialised unit at The Albert Road Clinic (South Melbourne - private psychiatric hospital). There is also the Bronte Centre at St Vincent's Hospital. Your daughter may feel better talking to other young people in her situation.
If your daughter is still unwilling to talk with these people, and unwilling to change her behaviour using Cognitive Behaviour Therapy, finding a therapist who uses Acceptance and Commitment Therapy may help. This therapeutic intervention emphasises focusing on what the client (ie your daughter) feels needs to change. I know a GP who worked with a young girl much like your daughter who didn't want to change her eating, but he managed to "connect" with her desire to improve her family and peer relationships (which was a 'side door entry' to the eating disorder, as opposed to the 'front door entry' most people took with her). The GP has his own website, Home | ACT Mindfully | Acceptance & Commitment Therapy Training which details the therapy and lists therapists.
This is really hard, for all of you. I would advise asking any of these people/agencies about support for you and your family, as well as your daughter. The treatment for anorexia often involves family therapy, since eating disorders affect the whole family. Good luck with this, and I hope I've been remotely helpful.
Faith
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