Absolutely let her buy it. It's money that's been gifted to her and all the other young girls have it including my daughter who bought it last week off her Xmas money
Christ can we stop this 'gifted' lark and just say 'given'. 
What is WRONG with parents these days?
You are supposed to be a parent! Allwoing your child to buy make up at an obscene price is madness. How can they learn the value of anything?
I like make up and have not even heard of the brand. I once bought a Dior eye shadow palette and felt guilty for months even though I could easily afford it.
I'd be encouraging someone aged 9 with £50 quid to save some of it for their first car, or a house deposit, or towards something educational.
I'd not be encouraging them to waste it on make up.
I also think it is completely wrong for a 9 year old to be allowed to wear make up except as dressing up.
If I saw a child that young wearing make up, I'd wonder WTF her parents were thinking of.
It's along the same lines as when some stores were selling padded bras for young girls who didn't even need a bra.
Sexualisation far too young.