This is not in any way "an important step in self care" at all, in fact it is the total opposite.
None of the much people smear on their faces has any benefit, other than actual medicine
Why do you want to start her on a lifelong habit of pouring money into companies that con her, and smearing useless pointless chemicals on her face,
This is pure misogyny and worse because it is coming at her through her mother.
YOu are teaching her that her own face isn't good enough, and she MUST conform to sexual stereotypes and she HAS to spend time and money putting muck all over her perfectly good enough skin, and she isn't good enough if she doesn't.
She is 9, for goodness sake
dont start her off on any skin care at all, and if you feel like you must do it yourself, do it out of her sight.
Hopefully she will never fall into the trap. But if she does, at least you will have a clean conscience that you didn't force this oppression onto her