Of course it fits. I am a girl, 1,57m (must be about 5'0) and I own this bike for quite a while now. First it was my bike to get to work with, now it's on the Minoura trainer.

I already have a "bike that was meant to be fixed": a custom made white track frame, which is a bit bigger than the violet bike, but fit's, too (just to make it clear again). Nevertheless, since it's a trackbike frame the bottom bracket is not that low.

And this was my own concern. I've seen lots and lots of fixed road bikes already. As long as the drop out is a horizontal one this really isn't a big problem.