I'm writing this as someone who suffered both anorexia and bulimia between the ages of 15-18.
For me, it did start with a need to lose weight. It started with gastric flu which made me lose about a stone in a week and upon my return to school, rumours has done round about why I'd be off ( drugs/pregnancy etc). I became isolated from everyone apart from my long term boyfriend, and the pressures of my GCSE's crept in; being told you are 'expected' to achieve certain grades is horrible, especially if you are, as you say your daughter is, a high achiever. Because I couldn't control what was being said about me in the classroom, or the way I was treated, or what I was expected to be, I looked to control what I was eating as it was the only thing I could control. It soon escalated into how low I could get the number on the scale, weighing myself in excess of 50 times a day ( before and after purging), to see what I could achieve, because no one could set the target but myself.
My mum struggled, and blamed herself for being away from home so much ( commuting to work 5 days a week) and me being left to my own devices; it wasn't her fault, and I can assure you that it's not yours. The best way you can help your daughter is to hold her hand, and be supportive of her recovery, but not pander to the ED behaviours. I went through a year of weigh ins, counselling and meal plans before any improvement was seen, which then went tits up when my boyfriend at the time told me that he preferred me being emaciated. I do not blame him for my relapse, because my eating disorder was very tough on him too, so please try to help him understand what she is going through and how to support her properly if you feel that's something you can do.
Limit commenting on food and weight to a minimum, along with clothing and sizes. My Grandmother, though trying to be helpful, would talk about food constantly ( she was overweight and trying to diet) which allowed me to indulge in ED behaviour by spewing information about calories and content. The therapy helped, although I struggled as I felt patronised by my therapist and ganged up on in family therapy, which resulted in me walking out several times, but it was the support of my mum which got me through it. I had a lightbulb moment after collapsing in a supermarket the day after being told that my chance if having children was significantly reduced which made me realise that I needed to get better, for myself, because all I'd ever wanted to do was be a mother.
It was hard, and I've had several blips, but I'm sat cradling 12 week old DD as I type this and it's been worth it. Since having her, I finally love my body, wobbly bits and all. Although I know there will be moment and days where old Ana creeps back in, I am strong enough to know I'm worth more than that. I wish you and your daughter all the best 