OP, my DCs are at a mixed day/boarding school. There are usually a couple of children in yr3 and a few more in yr4 who switch to boarding, usually on a flexi basis initially, then one or two take the plunge and the rest stay on flexi. Yr5 is when it starts to pick up. The girls tend to be ready for it before the boys (from what I can tell).
One of the teachers at this school happens to be a close friend who has known my DCs for 4 years now, She also happens to be a housemistress. Her view is that if the child is keen then the only suffering is on the part of the parent, but that if the child is not keen it can be very sad, because the child always blames himself for doing something wrong in some way. She also gets desperately sad for parents who have sent their children away to avoid big marital issues and 'life event' problems, because the children always pick up on the vibes but are too remote to get enough of the picture to enable them to process and understand things in real time - everything gets warped and misinterpreted.
My DS (similar stage to your DD) asked if he could try it a while back and when I sought the advice of my friend (who is currently his form teacher) her face lit up and she said "Oh God, Squiffy, let him go for it, he will have such a fab time", then a while later she said "But you do realise that he'll have so much fun that you might start to lose him, don't you?". I guess I am trying to say that it's horses for courses, and so long as your DD knows she can change her mind and switch to day or flexi then I don't think you have anything to lose, surely?
BTW, having done the career thing myself, I do agree with those posters who are suggesting you look at changing your own life. Sometimes we think that our career is our means of holding on to some semblance of 'ourselves' when the world conspires against us, but you really should think about your own options. No job is worth getting so ill over, and I think the stresses you currently have will be replaced with other stresses in an instant unless you get your work-life balance sorted (and believe me, I do not say that lightly, I'm forever banging on about keeping your career going).