As many of the others say, she sounds just like me as a little girl. I was also very bookish and didn't see the point of having friends just for the sake of having friends.
If you are sure that this is her choice and that she is happy being like this then accept that she is an introverted personality and work around that fact. You won't be able to change it, certainly not by arranging playdates with a group of bouncy girls whose interests she doesn't share. She will probably have a miserable time wondering when she can get back to her book and have a bit of piece and quiet.
I am guessing that you perhaps have a more outgoing personality than she does? If so, imagine a group of people of a type opposite to you (dare I suggest trainspotters as an exmample?), and then imagine having to spend a day with them, and you get the idea!
There are many positive aspects to being an introvert, for example they tend to be quite self-sufficient which I think is a real boon. Concentrate on the good bits rather than worry about 'negatives'.
I would certainly encourage her to join some sort of club or do an activity but it has to be one that she is truly interested in, because that is where she will meet friends that have interests in common with her.
And rest assured that she will meet and make fast friends, but only on her own terms.
I'm sure she will turn out smashing, but I wish you both lots of luck anyway!