When you say behaviour is so good you don't feel they should need such firm discipline at your dd's school, what kind of harsh measures are you talking about? Being told off for talking and threatened with detention doesn't seem very harsh to me; those would be normal expectations for a state school, too.
My ds (now in Yr 9), who is a pleasant and polite boy, has not only had several detentions in his (fairly ordinary) state school but has been put on report for persistent talking and failing to pay attention in class. It isn't because they have problems with discipline in general, but because they pride themselves on offering a good learning environment for all their pupils.
It has taken a couple of years, but I think the message has finally sunk in that being able to listen to the teacher undistracted is a perfectly reasonable expectation on the part of his classmates, and that for every other pupil who is egging him on there are probably two or three who are seething in silence.
Ime Yrs 7 and 8 are very much about adjusting to a new stage in life, learning to take responsibility for the way you present yourself rather than being nudged forward by the adults in your life.
I would sit down with your dd and say something along these lines:
"Of course I can't know what your teacher is like or whether he is a bit stressy. Again, I can't possibly know what your friends are like or if they're better and worse than you. But then that isn't really relevant. The important thing now is that you make sure you are making the most of your education and not disrupting anybody else's. Give it another month: make sure you never speak when you are not supposed to, give your friends clear signals that you will not be dragged into this, never respond if somebody else is being silly in class, work as hard as you possibly can in class, throw yourself into the subject- and if you are still having problems by half term, then I will go in and speak to the school."