My hair's currently about an inch or so longer than that. I normally wear a wig unless I'm doing boystyle (which would look really good on you, go for it!). A wig makes it really easy to change your look, which is also a plus. I'd use one even if I still had long hair, because my hair tends to loose any style I put it in very fast.
I have on a few occasions seen girls with short hair, you just have to be careful in the accessories you choose. They have short hair section here, though some of the styles I really wouldn't consider short, and a lot of the girls aren't wearing lolita. But it might give you an idea.
< this style is pretty close to your's, and is incredibly cute with the headpiece.