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A space heater is really the only best way to heat just one room. I don't see the hallway idea working too well because if the door is open the heat will just escape to other parts of the house. Because your daughter is so young and curious a space heater within reach of her (on the floor) is a big no no as is putting it on something it could fall off of. Personally if I was in your shoes and really didn't wanna bite the heating bill bullet I'd get an electric space heater put it in the middle of the room, build a nice good size enclosure for it (not to small, don't wanna make it hot or catch fire) so she couldn't get to the heater inside, and kid proof the cord by securing it from being pulled out and put it under one of those cord protecters that offices use so people can step and run over the cord without damaging it. Dunno if you care for that idea but to me it's probably the safest way aside from biting the bullet.
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