Im sure simon's post was helpful but because you are new, i will try to explain what you need to know. Just in case you need more than a plugin
Paint.net uses actual transparency rather than just making your secondary color transparent like in MSpaint. If you can see that checkerboard pattern where your selection was, that is transparency. What i would recommend would be to make a new layer( :AddNewLayer: in the Layers Box), then put what you want to move on that layer. You can then flatten the layer by clicking :MergeDown: in the Layers Box. New layers have a fully transparent background while the original background on the first layer is white.
I hope that helps but if you have any more questions or still don't understand, just say so.
BTW, that is a sweet Skyline.