I'll split it into games your daughter could play, and some that could be fun to watch and get her to interact with. This is coming from someone who was playing Pinball 3D in preschool, so your mileage when bringing up a gaming child may vary.

One thing I haven't seen here is casual games. The less deep stuff that can still provide a lot of entertainment for kids that may just be starting to get a hang of things like computer mice and keyboard controls.

Alice Greenfingers (1 and 2) is a casual farm game featuring the titular character starting her own farm and selling the produce. No keyboard controls, just mouse controls and it was a pretty great introduction for me as a kid to finer motor movements.

The Diner Dash series is also a pretty good one to start. They have some variations, I know there's a detective game under the franchise that you could get input from your daughter on as you go through to encourage interaction.

There's the FATE (the WildTangent one, not the anime one) games, where it was one of the first games I remember that let me create my own female character. It's a diablo ripoff with much simpler mechanics. Gameplay can be repetitive but it's still a very fun, mouse-heavy game I still go back to. You can also choose between a cat and dog pet, and feed them special fish you find to turn them into awesome creatures like flaming unicorns!! (I'm sorry, I really love this game) i it's certainly playable with not much reading skill and therefore should be okay for a child, even if there's your standard combat violence.

For games that are fun to watch, I remember playing a Hello Kitty game for the PS2. There's still elements like hitting things, but it's overall a much cuter aesthetic.

There's also a PS2 Avatar: The Last Airbender video game that's based on the show (highly recommended watch even for kids), so you could relive the show you've just watched by playing the game with them. It's 2 player.

Crash Bandicoot Warped - while you play often as Crash, in the latest game I think it's possible to play everything as his sister Coco, who was already the only choice for some stages in the original game. Violence is mild, and was also one of my early games growing up. Fun to watch and play for kids.

I think there's a game called Infinity Nikki (PS4, PS5, PC, Android) that's a dress up platformer game. New outfits unlock different skills. The only issue is I've never played it, and it seems like microtransactions may inevitably come into play. Take caution. It's a crazy pretty game, though...

The Marvelous Miss Take (PC, and some consoles iirc) is a stealth game about a young woman trying to pull off several art heists. It features a female main character and is generally quite fun.

Hope this helps :)

I wish you guys all the fun!