When my little ones were around the age of your daughter (5 or so) they were very afraid of monsters in the bedroom closet and also under the bed.
So I put water in a spray bottle with a drop of blue food coloring. Put a label on it that said "MONSTER SPRAY" and each night, part of the bedtime ritual was to brush teeth, a spritz of "monster spray" in the closet and under the bed and then tuck in and read a story.
I think the reason it worked is that rituals lessen night time anxiety and that the "spray" equated in their minds to "doing something about it".
So perhaps there is some soothing nighttime ritual that would make your daughter feel empowered and soothed?
The bottom line is that she is displaying age appropriate behavior in equating her free floating nighttime anxiety with some amorphous thing.
Whether she calls it demons or monsters, its what they do at that age.
There have been some great ideas given in above posts for helping her to understand real from not real. Unfortunately moms not helping but your daughter will put huge stock in what you tell her because it will be honest.