Your daughter sounds EXACTLY like a cousin of mine.
My cousin is/was an avid reader also. She would have her nose in a book while she was in the pool, while she was in the car, any free moment she had, she was reading. She read more books by the 3rd grade than I read in my entire life. She never really had any friendships either. And it was exactly as you described. It was almost awkward watching her try to interact with others her own age. She, too, is very intelligent, and always made good grades in school. People always liked her because she had a good disposition, but she just never seemed interested in being very social. She, too, tried lots of activities over the years, but her one true love was reading, well, and God.
She ultimately went on to college to be very successful. She earned a degree in English (big surprise), joined a sorority, where she held many advisory positions, and eventually, after graduation, became a campus minister, where she spearheaded a program for introducing fellowship to college students.
Even though she wasn't very social as a child/teen, she did grow to develop some very close and fulfilling friendships. She is truly a lovely person, and everyone who gets to know her, loves her. Not because she is overtly social, but because when you talk to her, you know she is interested in what you are saying. Because she is loyal to a fault. Because she is kind and loving, intelligent, and funny.
She has always marched to a different beat than most of us. But she is happy, and is just a wonderful and unique young woman.
I worried about her growing up (she's 10 years younger than me), because I thought she needed friends, she needed a social life. I thought she must be lonely. But now I'm learning that that may not have been true. She found her peace and fulfillment in ways that I didn't understand. And that's ok.
And she is truly one of my favorite people in the world.
Your daughter sounds a lot like her to me, and if that's the case, don't worry. She'll be just fine. :)