How old is your daughter? Sounds like she's maybe still at school? My dd was 19/20 and at university when the anorexia really took hold. So some of this may not be relevant to you but this is what helped her recover. Also, as you're a professional, apologies if some of this is stating the obvious.
1 Realising and fully accepting that she had an illness
2 Seeking help - just seeing the GP for the first time was a huge breakthrough
3 Going for an appointment to our local in-patient service (she was never admitted but only just avoided it) and seeing some of the patients and how ill they looked. That was a wake up call, she knew she didn't want to be like that
4 Having a plan. Seeing the uni health team regularly, going to her appointments, even just going to get her bloods taken, she looked at each one as a step forward to being better.
5 It took a while for her to see a therapist through uni so we paid for some private appointments with a specialist (not an option for everyone, I know)
6 She read some really helpful books. I'll see if I can find the others but this one seemed to be particularly helpful
As for you, the only advice I can give you is to be there for her. Sometimes you'll just have to listen, sometimes you might need to tackle the things she's saying head on. I often used to say "this is the anorexia talking, not you" and that seemed to work (sometimes). Sometimes you just have to wait for a horrible period to pass.
Also, please talk to other people about it. It really helps for you have an outlet too.
The thing with anorexia is it IS a battle against the disease. My dd used to say "there are two sides of my brain at war with each other". Sometimes it's a full-scale war zone, other times it's just a distant rumble in the background.
I wish you both all the best. If it helps at all, my dd is thriving - she finished her degree, is now doing a post-grad and is really settled and happy.