Exactly. Yes, it's a wig--I'd like to buy her a shorter one, this one is very very long and kind of gets in the way a bit. You can also style it, but if you don't stick it to her head with some double-sided tape, it can be a slippery devil.
I think glass eyes might be movable, but I'm really not sure. They look more realistic, I think, and they catch light better, so if that's a factor... These dolls certainly are customizable from the feet up, though. I would recommend a smaller one, though, say a 41cm doll.