Although you may want to leave the door open on your child's bedroom at night so you can easily hear the child or check on them easier you really should shut your child's bedroom door at night and even your own door should be shut at night.
It's really a safety reason in case of a fire which I would hope would never happen. But if you or your child's doors are shut then you have a better chance of surviving and escaping the fire as it prevents smoke as well as the flames from getting to you or child's bedroom as fast as it would if the door was open.
If you're unable to get to your child's bedroom through the bedroom door then you should get to them through your child's bedroom window.
If possible do what you can to get them out of the house before the fire department arrives since seconds matter.
Always keep your child's bedroom door closed for safety reasons. It's really easy to just open the door to check on your child in the middle of the night as well.