That's not going to work very well because the open door will let all the heat right back out. A space heater in an unattended child's room is dangerous, no matter what you do to keep the kid away from it. The things can still sometimes catch fire even if you don't knock 'em over.
You need to run a zoned heating setup. It's not that hard to do. check here for info.
http://www.smarthome.com/howto11.html