Sorry about your bike. It looks both nice and very practical.
If your bike is like similar bikes found here in Sweden, your dropouts are probably forward-facing. That is, the wheel falls out when it moves forward. If you buy a similar frame with the same dropout width, it'll be straightforward. If you buy a track-style frame, you'll need to buy a new anti-rotation washer from Shimano for the hub that matches it.
I would also be sure to match the style of brakes that you have. Clever dynamo wiring may also be a concern, or you may wish to just zip tie new wires onto the frame and fork. Some single-speed bikes have narrow tire clearances, and no provisions for fenders or racks, or lights... you'll want to keep an eye on stuff like that.
No aluminum frame should ever be re-spaced in the rear to fit a different width hub. With steel, it can be done by an average, drunk, home mechanic like myself.