The thing is though- your daughter is actually right- not necessarily (hopefully ) right about any current situations leading to a nuclear exchange.
What she's right about, though, is that nuclear weapons are utterly terrifying, immoral and auful and it's beyond insane that we have them ( I mean 'we' in the sense of human society generally) .
Russia and the USA have thousands each. They are all a lot worse than the bombs dropped on Japan, at the end of ww2.
The answer is getting rid of nuclear weapons and making them illegal- not calming ourselves down and pretending 'every things ok'-because it's not ok-.
I remember reading the book 'Hiroshima' when I was 12 in the early 80s my mum said, was I a bit young to read it, she didn't want me to be upset and I remember standing in the kitchen saying that children younger than me- babies even, had died in that attack and if they were old enough to be killed by a nuclear weapon, I was old enough to read about it. To which my lovely mum had to agree.
i still remember that summer, at various points looking at the adults around me ,in the nice little village I lived in-how they almost disgusted me by their stupidity and complacency -why weren't they doing any thing? Why were they just acting as though everything was ok, when it wasn't?
I understand you don't want your daughter upset- but the truth is -it's an upsetting situation- if everyone who cares about it, is told not to worry- how will we ever change any thing.
You could, perhaps, as well as trying to help her not be too worried now, talk to her about people being able to change auful things in the world, maybe she could join CND, or start an anti-nuclear group at school.
Maybe find her some films on youtube or books about the anti-nuclear movement.
look how much little Greta has made her voice heard. People can make things change- nuclear weapons are made by human beings, they don't grow on their own like mushrooms! That means any time enough people say 'no, we're not having this, any more' we can get rid of them,it's how women got the vote!They talked about it and got out and wrote letters and marched and some were prepared to go to prison about it, and eventually , things were changed.
You know your daughter, obviously and try and make her calmer and happier, right now, tell her not to worry too much and give her a hug, but please-if you feel she is at all 'up to' dealing with it-don't persuade her not to worry or care at all- because somehow things have to change.
Your daughter's response to nuclear weapons and nuclear war is actually the appropriate one, it's the adult world that is wrong, and needs to change.