Choice of wire diameter for doll's house?
I always like to consult this chart https://www.powerstream.com/Wire_Size.htm
So I would go with at least 27 gauge wire. It says it has a maximum current of 1.7 amps. This may also be different depending on how easily your wires can cool. If they are in plaster that may insulate them so you may have to go thicker. If you are using 24 Gauge I would think that would be fine.

Another note, if you use DC that will generate more heat, if you are only powering LED and incandescent bulbs why not use AC? AC will allow the wires to stay cooler. The LEDs may flicker but it shouldn't be too noticeable. If you have a 12 volt AC adapter that keeps the output AC I would try that out.