My dementia patient startles very easily. How can I protect her from falling?

Yes, I'd ask doctor for help on that. It sounds like she's really anxious. Also, just to let her know where you are, you might get some little bells to put on your shoes, just so she can hear you coming down the hall.

Perhaps she needs medication for her anxiety, is her doctor aware of it? And this may seem like a silly idea, but if she startles so violently whenever you enter the room she is in perhaps your could make a habit of singing (humming, whistling) so that she can hear you coming.