What PTC/Fuse would you recommend? what model etc.
Any ideas for LEDs are welcome as well :-)
It depends - if you stay with bulbs then they might pull 40-50mA each at 12V. With modern white LEDs then you might find that each LED might be as little as 1mA. You can probably drop to 6V supply too. Each LED will need a series current limiting resistor, probably around 750R to 1.5k (experimentation needed).
If using LEDs then probably the smallest current PTC you can find, say, 50mA would provide maximum protection for the (thin) wiring and batteries.
As far as LEDs, ebay is your playground. I don't know what your fine skills with tweezers and soldering are like but you could probably use 1206 size smd LEDs glued to the ceilings and soldered with fine wire (the resistors could probably be smd too). If you are less good, then wire ended 3mm through-hole parts (wide angle). SMD would be neat though. Maybe you can do uplighters / table lamps too.
You are the first generation who can realistically implement LED lighting in a dollhouse for your children - let your imagination go wild!