Am I safe using the cable I've got laying around,
Nope.
or is there some magic involving DC and AC?
It's not an AC vs. DC problem. It's that the thing that determines whether a cable is suitable for the job has much more to do with the current flow than the power. So you almost don't want to pay attention to the power being conveyed, and only pay attention to the current being carried.
Things get a bit complicated with cables, because you're partially worried about the voltage drop in the cable, because that voltage drop means lost power, and you're partially worried about the cable heating up and catching on fire. The cable heat problem gets even more complicated because a bunch of conductors in a bundle can't dissipate as much heat as a single conductor in free air, so the middle of the bundle may get too hot.
The bottom line is that you need heavier gauge wire. Secondarily, you can probably get away with insulation that's rated for a much lower voltage than your "household cable" (which, I suspect, has insulation that's good for 600V or more, if the European authorities are as conservative as I expect them to be with house wiring).
I'm not sure about Europe, or if huishoudsnoer is the cable you find inside the walls (as opposed to lamp cords). In North America the typical house wiring is solid; inside of devices people generally go with stranded wire so that ordinary motion and vibration don't break things.
Around here the best place to get stranded wire that's good for carrying that much current in a 12V environment is the local auto parts store. Some places even label the packaging with the current-carrying capacity. If you don't want to do that, then you need to order some from whoever is the usual suspects over there.
Note that the stuff that's good for cars is not what you'd want to use going to the print head, or anywhere else that the wire is being bent all the time -- that requires special wire (called "continuous flex" in English) that uses extra-fine strands, a special alloy of copper, and special insulation, all so that the wire can be in constant motion without breaking.