To be quite honest I did not read through all the comments to see if this has been suggested already, but Child of Light comes to mind!
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Red Alert has a strong female character and is definitely age appropriate... :)
Lots of great suggestions from others already, so I'll add some for when she's a bit older. I'd say when she grows up the Tomb Raider series would be great for her to play if you want a good female protagonist. And it may be too raunchy of a recommendation for a daughter, but if you want another good female protagonist I'd suggest Lolipop Chainsaw, a great game for when she becomes a teen if she keeps up the hobby. :)
I originally bought this game years ago to play co-op with my then girlfriend, but I think it can work for your purposes too - Never Alone
They're not particularly old. There's a few games as recent as this year there. But then, can you really trust the quality of a list that includes 'Laura' (sic) Croft?
What platforms do you play, and how old is she? Because there's no point in us recommending particularly grisly PS exclusives like The Last of Us Part 2 if you're an Xbox player with a 6 year old.
Ugh, sorry - my original wording wasn't clear. I meant "too old for her". Post has been edited
If you're okay with some very black comedy (all spoken-aloud, nothing shown) and the occasional blood splatter when you get shot, the Portal games are good. The villains are robotic turrets with machine-guns that are defeated simply by tipping them over - so while they're acting in very violent and lethal ways, the player is just teleporting around and nudging them over to fall down onto their side. But I remember my kid being very offended when GlaDOS called the player character fat, and later reveals she mass-murdered a building full of scientists using nerve-gas.
Half Life Alyx + No VR mod
My 2 year old enjoys watching aloy go on a killing spree in horizon forbidden west..... I am a bad parent.
Street fighter 6. Pick Juri, Kimberly, Manon or more. With the new Dynamic control system, even your kids can easily play with you.