I think you might be mistaking introversion for being "behind" socially. It's not, it's just a personality type. Your daughter sounds a lot like me through childhood, and for me it got much worse in my teens because my mom was desperate for me to "succeed" socially, and I started feeling wrong for being shy.
I always did well when there was a focus on a topic of interest, and not just "socializing" for the sake of being social. This can be the gift of Asperger's (very high-functioning autism spectrum) and it truly is a gift, if treated that way. Many highly-successful geeks are "Aspie" types, and I think if the designation had been available when I was young, I would have been diagnosed with the syndrome.
Now that I've grown up, and am able to shape my life in a way that is comfortable and satisfying for me, shyness is not a big issue. I am watchful and quiet in social situations, which I avoid when possible. I am reluctant to make phone calls, but can and do when needed. But without my mom pushing me to be what I am not, I have become much more comfortable in my own skin and capacities. As far as I can tell, I'm a much appreciated friend, because I tend to listen much more than talk. I LOVE keeping the spotlight on other people, and they generally love it, too.
So I guess I have this dangling question. Does your daughter seem unhappy having few friends? She might be perfectly fine being creative and taking art and nature classes. That sure would have worked for me!
ADDED: After reading your update, I remember sometimes feeling sad that acquaintances got invited to parties and I didn't. Everything in life is a trade-off, though. I heard many years later that a very social acquaintance felt sad that I seemed so self-posessed, while she felt like a shallow social butterfly. That perspective probably would have helped me when I was young – I think I would have realized that every life has strengths and weaknesses, and nobody is always happy, no matter how they appear from the outside.
I'm thinking of a terrific book called Please Understand Me that helps you locate your type in the Myers-Briggs personality universe, and helps you understand how you and others fit together to create the whole of human experience. I highly recommend it!