Girls + their age = whining, or that high pitched voice.
The book "Your 6 Year Old" , from www.amazon.com is great. Its a series of books in each age. Although written years ago, it is still pertinent. And explains simply what each age goes through, and how they understand the world.
Next, my girl is like that too. BUT... I understand that sometimes, especially when she is either (1) tired or, (2) hungry, she whines. I/we always encourage our kids to express themselves... but for this "whining" thing... what I do is: I tell my girl "Okay, you are in your yah-yah moment. You can whine for 5 minutes, and get out your yah-yahs, then that's it." And OFTEN times, this works, and she will deflate, then feel better afterward. Then after that... we do our thing where if she whines/gets high pitched... she can go in her room and just yell it out/whine. As long as she does not take it out on others. This works for us.
AND she has gotten much better... she does not do it so much anymore.
Kids often need to get out their "pent-up" whatever. For my girl, I can more or less predict when she will get like this. So, we trouble shoot THAT... instead of just punishing for any little voice inflection that is "irritating." Because as our girl "explained" (we asked her why she does this), and she says "I can't just control it all the time, I'm a little girl, not a grown up.... even you/daddy gets icky too sometimes..." (uh yah, she has a point). But we emphasize that she "practice" her voice.
What ALSO helps it, kids this age don't always have impulse/emotional control yet... and they can still be impulsive. So... what we do is, when our girl gets like that... I say "Redo." (which means: okay, try and say it in ANOTHER way... you have a chance to 'redo' that voice/sentence/request, etc.) And, this ALSO 'teaches' the child "how" to use their voice... more pleasantly, while still being able to say what they feel. Thus, they get validation.... which is often why they get frustrated).
If she is doing this in school... she has to learn otherwise she will disrupt the other kids. Perhaps, if she can learn to gauge herself... and then, do something else, instead of the whining? Like, take deep breaths. Which helps the "stress levels" in anyone, even adults. Then again, some Teachers will either ignore that particular child until they interact more 'pleasantly' or they will get time-out, or placed somewhere else... if they are disrupting the other kids.
Have you asked the Teacher how she handles kids like that?
My daughter has a class-mate like that... (a 7 year old boy), but per privacy issues, I don't know what his problem is. But, he actually cries/whines/tantrums when he does not get his way. And it does un-nerve the other kids. I think he sees a counselor.
I think, teaching how to express their feelings appropriately, 'allowing' them to feel understood, creating an alternative way they can let out their yah-yahs, and just plain not giving in, are ways you can trouble-shoot it.
I'm sure other Moms will have LOTS of other suggestions too.
Or, ask your daughter WHY SHE GETS LIKE THAT... and let her think about it, and explain in any way she can. Then ask her "HOW can you feel better, instead of whining/tantruming?" She may not have a pat answer about it, like an older child... but just as a way of feeling it out and 'seeing' what she is thinking.
Since time-outs and taking things away from her does NOT work... nor encourage her... how else can she realize it? Is is just her personality? Or temperament?
The book "How to talk so kids will listen, and listen so kids will talk" is also GREAT. You can find it on Amazon or any bookstore.
I know, its not easy.
Just some ideas.
All the best,
S.