Okay, I really think I'm slightly insane. I looked for guides like this one, but I just can't find that on my 2DS camera software.
As I can't find such a guide for the Nintendo 2DS, I think that it uses the same software as the 3DS.
This is what guides tell me to look for in the camera software:
But I just don't have this button visible. This is how my camera app looks in the bottom screen:
That parrot gives me some basic help for the camera, but there seem to be no magic to morph him into a QR code button. How to achieve this?