I would wear it, if I had legs as nice as yours, with sheer tights, knee-high boots (preferably not black) and some elegant jewellry. It will be a fine line between slutty and elegant but I think the point of a little black dress is to find that line and trace it. If you feel uncomfortable about how short it is (and it is pretty short) then wear black tights.
We need to see a front view of the bottom of the dress to really judge how short it is, though. From the side view it looks about long enough to get away with.
On a similar note, a girl in my english class came to college a few weeks ago in a jumper and tights. That is it. The jumper was shorter than the afore-mentioned dress and the tights were not opaque. Apparently she couldn't find her shorts.
My question is, if she needed to wear tights with her shorts (and boy did she need to, it is VERY cold here at the moment) then why wear shorts? Or rather, why wear no shorts? What is wrong with trousers? Is this just me? Is it stylish to wear tights, shorts, sandals and legwarmers?