At our elementary school, each grade has a "social" starting in Kindergarten. They're held in the cafeteria with all the lights on and the parents standing around watching it all. They hire a DJ to run music and fun games for the kids and it's a big, fun party - and the kids are all so cute jumping up and down to the music!
In 5th grade, the "social" is the "graduation party" held on the last day of school. It's a big deal. Girls wear nice dresses, boys wear ties, etc. It's held at a rented place off campus and is quite fancy - and no parents, except for the chaperones. Last year, there WERE some boy/girl pairings. My daughter didn't go with a boy, mostly because she just wasn't into boys and wanted to have a good time with her friends. She said that the girls who went with boys were all about the drama "Nick isn't paying attention to me!" "Tim just wants to hang out with his friends and wont' dance!" etc. That kind of stuff bored her. She DID wear a strapless dress, which was extremely cute (I have no problem with girls showing off their shoulders, now if she had any *cleavage* showing, THAT would have been a problem for me). I'm glad I didn't have to deal with the boy thing, though...
This year, as a 6th grader (which IS middle school in our district), there have already been a couple of socials. They're fun for the kids and I've never heard of anyone acting inappropriately. They've all been going to these yearly "socials" since K, so by now, it's no big deal and they know how to behave and what's expected of them.
Of course, it's purely up to you, but if you think your child is responsible and would enjoy a dance with her friends, I don't see why you wouldn't let her go. She needs to learn these social lessons at some point and you can help her navigate through this more easily while she's young. By the time they're in HS, things will be different and your influence won't be as strong as her friends. NOW is the time to teach her appropriate behavior at school functions. Plus, she will have so much fun and will ALWAYS remember her first school dance!