Parenting: Elementary Ages Community

Hello all,
I have a daughter in 5 year old Kindergarten (she just turned 6 in January). I really need help with a social problem she is having at school so please bear with me as I want to give you all the information I can think of that may help.
She is a great kid (obviously I'm biased) but we've never had any issues with her in the way of behavior. She's an only child, average height, normal weight, and is very polite. We live in a very small town, and she attends a very small school (4K-12th grade in one building). ?She has a cousin that lives down the road from us, but other than that she doesn't get to play around others very often, just school mainly. She was never in and is not currently in daycare, or part of a play group or anything. (as I said...small town)
I was a stay at home mom until this past fall when I started nursing school. However, I did not consider this to be a huge change in our lives, as I only go a few days a week and only once a week am I gone when she is not at school. I get done at 5pm. On these days she stays at her grandmas house (also next door to us) for about an hour until I pick her up. (I should also mention that where my husband and I live is next door to my father in law on one side of us, my mother in law lives next door to him two houses down with my sister in law [mother and daughter living together>, and two houses in the other direction is my sister in law and husband/kids. We all happen to live right in a row of each other because my father in law owns quite a bit of land on the street, and has parceled some of it off to all of his three kids and they all decided to put houses on it-- 4 houses all right by each other within walking distance)
She has always been a great behaved child, she always says please and thank you, I can probably count on both my hands the number of time outs she has had in her life. She's just a very sweet girl. Parents often remark to me out in public at a place like McDonald's play place or walmart what a wonderful kid she is and how polite she is. I swear, I am not tooting my own horn, she's just always had a very polite, sweet disposition since day 1.
She had a small problem with shyness in 4k, and perhaps the beginning of 5K. She tends to be a little quiet at times, and is shy approaching new children. Give her a boost of confidence and couple minutes though, and she'll warm up to just about anyone and go say Hi. She seemed to come out of her shell a little bit after the beginning of the school year went by. She talked a lot about friends, having fun at school, and I didn't suspect there to be any problems. Her teacher did say at the November conferences of last year that she tends to play on her own and needed a nudge to play with others. We discussed it but she didn't say it was a bad problem, just usually on days other than Mondays and Wednesdays. (Her cousin who lives a couple houses down from us is in 4K this year. 4K-ers only go to school twice a week and when her cousin goes on Monday's and Wednesday's that is usually who she plays with. They are very close.)
She's a very bright kid. She knew her alphabet, numbers, and letter sounds before 4K, and was reading before kindergarten. We just had conferences in Febrary again and her teacher is going to have her sit down with an assessor of some type because she is so far ahead in reading. Her teacher estimates her to be at a 3rd or 4th grade reading level. She is also doing very well in math. Her teacher said she has quite the imagination (which she does) and she "could see her growing up to be one of the brightest problem-solvers the school has seen" so we were very pleased with her. She loves to learn, and she often makes herself pretend homework at home. She is extremely proud of herself and is often proud to say "I'm so smart!" She's reading chapter books (slowly, but with minimal problems sounding out large words). She is taking our breath away!
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