Plastic surgeons are crafty buggers. They love sponging off poor girls like your daughter, they have no qualms, as long as they write to her GP saying 'she realises the pros and cons and her concern is mainly around her confidence' - they need to lie it is about confidence, not about looks. You won't get honest assistance from a plastic surgeon.
I don't know what to suggest, apart from asking her to google any potential side effects, sending her to a psychologist and explaining to her that in attractiveness stakes youth is everything - a fat, zitty, shy 18-year old will always trump any 25 or 30-year old with a model figure and impeccable skin. Try to explain it to her that youth passes quickly and she should enjoy it, every zit and every bit of fat on her face - tell her those 30-year olds have fillers to make their faces plump, making themselves into younger versions of themselves.
If this does not work, ask her to google 'revision surgery' - how many times patients are dissatisfied with the outcome and demand revision. Also, ask her to google the faces of plastic surgeons - they are all available - and ask her why are they all look like they never went near a knife? And then google side effects.
Tell her if she is not happy with herself, she should work on bettering herself, not her looks - do a meaningful degree or a meaningful apprenticeship, become useful to the society, help people. But be pro-active, don't be shy about voicing your disapproval - she is a child and a stupid one at that.