Her arms a little on the short side, yes. But other than that, it seems good. When drawing arms one thing to remember, though it varies slightly from person to person, is that elbows generally come down to waist level.
As for hair, drawing the outline of the hair is the way most people start, so you're onto something here. Once that's done you can then add the extra details.
I ahven't got much time, got to be out in a couple of minutes, so I'll leave you
this link for your attention. Should come in handy.