Speaking as a nearly 56-year old who is wrinkled, blotchy, and rough in patches due to age, sun, and wind damage...
I asked my dermatologist about this a couple of years ago. She told me, "absolutely not!"
First of all, skin peels are chemical burns! They actually damage the skin and make it more vulnerable to damage in the future.
NO reputable plastic surgeon/dermatologist would consider doing a skin peel of any kind on a 10 year old.
OK...you need to get your daughter off of social media ASAP! She is way too young for it. She is way too young for ANY unsupervised access to the internet.
Facebook requires that its users be at least 13. Did she lie to set up an account, or did you?
She is 10 years old. She is a child. You are the parent. The skin peel issue requires a one word answer: NO!
You are attempting to reason with a child where no reasoning is necessary and only weakens your position.
That said, I am concerned about the fixation on "beauty" etc., and am worried that she may be incubating a case of body dysmorphic disorder. She should be screened for that asap. 10 year olds can become anorexic, bulimic, etc.,
In the meantime, get her off facebook, control her internet access tightly, quit buying the magazines, restrict access to TV, and get her involved in healthy 10-year old activities.