Baby Chocolate's a doll

I was really surprised after my relatively short and bearable labour with my second child to deliver a baby girl.
I don't know why I was surprised, really. I guess having had a boy already, she was an unknown quantity. When the midwife proclaimed, "it's a girl" I didn't know what to expect.
Obviously when babies are immobile blobs, sex doesn't really make that much difference in their lives.
But when they start to get mobile, and specifically, play with toys, it has become more of an issue for me, at least.
To begin with Baby Chocolate* played with her brother's infant toys which are all gender neutral. Now she's reached an age where she has soft toys she favours.
We've had a couple of little baby dollies around the house among the soft toys (one of which was a hilarious joke gift for my husband when he expressed a desire to have children) and Baby Chocolate has taken to one dolly especially, cuddling her at night. But am I doing the right thing giving her the doll at all? Or am I, by worrying about it at all, a neurotic middle-class feminist who takes her amateur psychology hobby far too seriously?
Baby Chocolate's brother was mildly interested in the doll when I was pregnant and I was preparing him for a new baby in the house, but soon began looking on any doll with the pinched-lipped disdain he reserves for Dora the Explorer and the colour pink.
Baby Chocolate is in every other respect more of a what you might consider a stereotypical "boy" than her brother. She climbs like a mountain goat, loves cars and Lego, and lacks the caution and reserve characteristic of her brother.
Is her attraction to the doll predetermined, following the hypothesis that female humans are more nurturing? Or have I subconsciously foisted it on her because that's the way I was programmed?
Should I encourage or discourage this behaviour? Should it matter at all?
I confess to putting hair clips in her wispy baby locks, so I wonder if it's not just a contradiction** to even worry about a doll?
It's one to add to my list of quandaries.

* Not her real name.
** I reserve the right to behave in a contradictory manner whenever I like.