I am completely with you, Bernie. Yes, there are extremely high levels of toxic materials in nail varnishes, including those labelled "non-toxic" - that just means that they contain toxic chemicals in quantities that fall below the level that has to be labelled as toxic, but why allow any unnecessary toxins into our children.

My girls asked for beauty products when they were younger and so I bought ultra expensive, certified organic products as a special treat that would last for years. They were banned from ever doing their nails themselves and we only painted dots and tiny hearts at that stage. Being allowed to experiment did satisfy their curiosity and neither of my girls bothered choosing to wear make up until they were 18 and 16 respectively, even though many of their friends wore it for years already.

This article may be of use to share with your daughter:

https://www.drlamcoaching.com/blog/why-you-may-want-to-think-twice-before-painting-childrens-nails