I agree with a lot of what's said here .. But let me start by mentioning that my daughters are now 18 and 14, and totally different.
Starting at about the age of four, both girls wanted to imitate me by wearing my high heels and putting on makeup. They also wanted to use shaving cream and a razor like their Dad. Emulating their parents at this stage is how they develop identity.
But I was worried about "sexualizing" them... I think allowing little girls to wear makeup as a daily routine is inappropriate. Emphasizing lips, eyes, and the flush of cheeks is a sexual signal that's hard-wired into men's psyches.. Young girls should not be looking like that.
So, while I let them "shave" and put on makeup, it was part of a pretend/dress-up thing. They were never allowed to use real makeup, and never allowed to wear their play makeup outside the house. because it was only for "when you're older"
My daughters were allowed to wear tinted lip gloss when they were 12, and eyeliner the following year. My older daughter still only wears gloss and eyeliner, the younger one is begging for mascara, blush, sparkly body powders and bronzers.. the answer is still no. (I have however let her wax her uni-brow since she was 11).
Do what you are comfortable with but as another mom mentioned do not buy play makeup kits manufactured in China because of the lead content. It's better to buy hypo-allergenic makeup if you can't find play stuff that's safe.
Congrats on your baby boy.. and welcome to the joy of parenting a daughter... It's a wondrous challenge all the way...