This could be the early stages of schizophrenia.
I have catatonic schizophrenia myself and I remember well what it felt like as a child before I came to understand the illness. You've pretty much described it.
The disease varies greatly from person to person and a huge amount of what you see on TV or hear about in sensationalist stories/otherwise is completely false. Few people have much idea of what it really means beyond crazed maniacs in blood soaked lab coats wielding axes and intent on murder. Surprisingly enough this isn't the reality for most people.
I'd like to impart a few pieces of knowledge from my own experience -
1) Seeing faces for a fraction of a second is one of the most common schizophrenic visual hallucinations there is. Even I get them. They'll come when I'm tired and least expecting it - I'll look around, the duvet's creased into a slightly curious shape and they'll be this face staring back at me right there. Even as an adult it transfixes and terrifies me in equal measure. I'm genuinely terrified by it. But I calm myself, control myself, and move on half a minute later. Usually the face is a mash up of two or more people I know or have seen in pictures/videos recently.
2) Schizophrenic tendencies are extremely common across very large numbers of people in the population. Oftentimes symptoms are mild and only there when these people are at their most tired/stressed. Most of these people will live a completely normal life and oftentimes symptoms are so mild they'll never even get a diagnosis. Schizophrenia is not always life changing - in its most extreme form it is, but the majority of people who have it get it only mildly.
3) Schizophrenia/schizophrenic tendencies are very hereditary. It's impossible to say for sure from your account whether you and your wife might have had a trace of a tendency without realising it, but it sounds like you might have. If you do have a slight trace of hyperactive imagination running away with scariness occasionally, that could easily be passed on to your daughter. But that doesn't mean she'll be any worse than you and you two - if you had it at all - had it in a mild enough way that it hasn't affected your life. There's no reason to think now that your daughter would necessarily be any worse than that even if she does have a slight tendency.
4) Full on schizophrenia is usually diagnosed in mid to late teen years/early twenties, but as it's a brain development disorder, usually looking back in hindsight you can see the start of it much earlier. I started to experience a few tiny effects age 12, proper hallucinations age 16, and only figured out what was going on age 20 (i.e. diagnosis then). For those diagnosed a few years younger than me it's not uncommon to see first effects age 9/10.
5) If symptoms get worse it may be worth seeing your GP but there's probably very little they can say right now - they'll just say "maybe/maybe not", keep an eye and come back if things get worse. There's probably nothing a doctor can do right now. Your daughter would need to be a lot worse before they'd put her on anti-psychotics, so don't expect anything from the doctors right now even if you do go. They won't be able to tell you yes/no to schizophrenia. It's a possibility, but very much unconfirmed and too young to know anything at all. There's no real prevention possible - it'll happen or it won't as it may.
6) Tiredness plays a huge role in the blending of the dream world and waking life. I know it's difficult because nightmares are common, but make sure your daughter's well rested. Make sure she gets early nights for the next couple of days if you can. I know it's difficult (and I'm not yet a parent so no expert on bedtimes), but if I'm experiencing hallucinations or faces the very best thing for me is several early nights in a row. The more sleep I get, the less the dream world and waking world blend and the fewer frightening faces I see. If I'm well rested I don't experience hallucinations at all. Do not underestimate the power of sleep - my single biggest tip to you is that when the faces come, several early nights in a row is the very best prevention there is.
7) Don't be worried by this - my personal opinion is that your daughter does have a schizophrenic tendency. She'll likely always experience some level of minor hallucination when tired. If it progresses and gets too bad there are now very many really effective treatments your GP can prescribe if needs be with minimal side effects (weight gain is the big one - so very careful food control and dieting whilst on the drugs is usually vital to maintain a healthy body weight). But - schizophrenics are also often very bright people with high IQs, hyperactive imaginations and more likely to excel in subjects such as maths. Always be there to reassure your daughter if needs be, keep her bedtimes as routine as possible, make sure she gets an early night if the visions come, and contact your doctor if it starts to impact on her life in any major way. [In later years watch out also for depression which is very commonly associated and tied to schizophrenia for reasons not especially clear]
The very best of luck to you and your daughter though. I hope I can give you some encouragement that things will turn out alright either way - I have a respectable finance job within a large retail bank, plenty of friends (a small handful I've told, but most have never guessed I'm schizophrenic), one of the very top marks in the year group in a mathematics degree from a top institution, and a condition I simply refuse to allow to control me.
Feel free to let me know if you have any more questions you'd like me to answer.
(@moderators, please don't merge this account with my other one. I know I have a proper account with gold badges etc. on the network but I want to keep my medical conditions entirely separate from my professional online presence)