In true "WWYD" style, should my friend buy her three year old daughter some make-up for Christmas?

This morning a received a text from a really good mate:  
Random question.  Thinking of getting L a wee Hello Kitty dressing table and matching play make up case because she is obsessed with make up. Want mine back. Do you think she's too young at 3? Had a very interesting chat at work yesterday about it.

My first text back was almost "What's a grown woman doing with a Hello Kitty dressing table?" but sent this instead:
Honest answer - your child, you do what you want. Feminist answer - do you really want to express that make-up is an important part of life for some people to a 3 year old?

which seemed to get her thinking a bit deeper and her reply was:
Oooh very interesting point! As a feminist this resonates with me. Yet I do love make up.  Eek, what a dilemma!

But then this also got me thinking.  

I've been a HUGE fan of make-up from a very early age but had to be content with those Swizzles candy lipsticks for a time.  Then I was thrust into the blue/pink eyeshadow era that was the 1980s where everything was so wrong it was right.  My mum wasn't a great fan of make-up.  My few pointers came from a much-loved Aunt who was slightly closer to my age than the rest of my aunts and uncles and she bridged the generational gap for me.  As I explain in a previous post - Sans Fards - I use my make-up as a mask, of sorts and I'm rarely seen without it.

I do remember buying my daughter little make-up sets; you know the sort - the ones that promise to wash off but end up becoming a 'feature' of your child's face for a few days and the decor for a couple of years.  She was about eight or nine when she started asking for these though and not three years old.  However, take a look at when my granddaughters gave me a make over.  They knew where every different item went... well, in the face area at least.

So, seeing as though Tracy finished our conversation off with
I think there's a blog post in this for you!
I'd love to know what are your thoughts are.  Do you think that buying a three year old a make-up set is right or wrong?  What signals does it send at such an impressionable age?