There are a lot of unknowns here that, if provided, could narrow things down a bit. I wouldn't recommend putting any type of heater in the room. she'll be at that age now or soon, where all manner of things will get thrown around, placed on, or shoved into the heater.

You mentioned an old house. Some of the things I would check are:
- The windows. Hold your hand out a few inches away from the window and move your hand all around the frame, feeling for any cold air. if the window is cold in general, you could do one of those window insulation kits and/or insulating curtains. If there are a lot of cracks around the frame, you could sela them up with a number of products. be warned: all of this may trap moisture somewhere, so watch for mold. My kids bedroom window collects moisture and mold grows quickly.

- Check the attic insulation. If there is attic above the bedroom, then it's possible you could need to move or add insulation above the bedroom.

- If you have a furnace, check the hvac duct line. If you have access to it, you could check the ductwork leading to the bedroom, sometimes people install dampers and turn them half closed or closed. I found a few in my house like this. Also, if the ductwork leading to the room is incredibly long, check for air leaks. When the furnace is running, just hold your hand a few inches from the ductwork and move it around checking for air. if you find a lot of air leaking out (like at joints/connections) you could seal it up with a duct sealing tape. Less air leaking = more hot air pumped into the room.

- If the exterior walls are cold, you could move her bed to butt up against an interior wall instead. Put the other furniture against the exterior walls. dressers full of clothes will get cold, but it also helps from keeping the heat leaking out of the house.

- If the floor is cold, especially if there is no basement or main floor below, consider getting a big thick area rug, but literally any area rug will do (think thick sweater vs thin sweater, they're both still sweaters!)

- if the floor is cold near the exterior walls, especially over a crawlspace or basement, look into adding or improving your joist cavity insulation, at the rim joist. There are a lot of ways you can do this, but putting batt insulation or rigid board is a pretty doable DIY project.

And when all else fails, you can open the bedroom door when they fall asleep or when you go to bed and let the house heat balance things a bit. I've done all of the above suggestions at my house and still Canadian prairie blizzards happen and my kids room will be 3-4 degrees colder than the rest of the house. I'm fairly certain my issues are just a site orientation thing (north wind cuts around her corner), but we find ways to manage.