Many of the Ghibli movies should be perfectly fine (My Neighbor Totoro, Whisper of the Heart, Kiki's Delivery Service, Ponyo, The Secret World of Arrietty, ...).
As much as I am a fan of Spy x Family and Violet Evergarden, they are more for more mature audiences as they have quite the adult themes. Violet Evergarden is set in a war world and although the story is not set in the war itself, the flashbacks (especially THAT scene during the attack on the fortress) are nonetheless too violent.
Spy x Family might seem like a wholesome family anime but it has underlying political and war themes. Bond's arc as well as Yor's assassination techniques in Ep 2 is something that I would not really recommend to a nine year-old kid. There's car explosions and use of dogs for warfare
Spy X Family has some pretty dark storylines, hell episode one is one those very cases. I think it could be good for older kids and teens, but stuff like Bond's introductory arc is really heavy. I cannot imagine a kid reacting positively to the Handler's speech about her experience with war.
then i suggest elfenlied and euphoria if you want a troll here. Tthe second is weird porn, i only seen a warning but i still remember the name after years. So dont look it up when your are not into shit (right pronaunciation)
Cardcaptor Sakura and Sailor Moon were made with kids in mind, I think. Definitely seems like a lot of people grew up watching them.
Keep your hands off Eizouken is one of my recent favourites, and I think would be really enjoyable as a kid. Lots of imagination scenes and a really sweet story about friends.
Nichijou should also be inoffensive, just kid shenanigans. They don't always make sense, but the tone is very chill. Also Azumanga Daiou, similar vibes I think.
Paripi Koumei is a recent show about a girl trying to launch her singing career with the help of a reincarnated chinese general, I don't think it has any scary scenes but a lot of it does take place in a club, and depicts alcohol. But the story and characters are heart-warming and I enjoyed it a lot.
I've also heard very good things about Carole and Tuesday, which came out around the same time and also centres around music. But I'd recommend looking into the themes more, I don't know how serious it gets.
Hinamatsuri - I think this might be the funniest show I've ever watched. It cracked me up even on a rewatch. It does center on a Yakuza member, so there are some jokes that might appear scary, though being a comedy of course everything works out pretty quickly. It depends on her tolerance for those themes.
One I don't see recommended often is Gatchaman Crowds. I just looked up the rating and it is 13+, but I loved that show, and remember recommending it to my younger brother around your daughter's age.
I haven't met a 9-year-old in a while, so sorry if my recommendations skew a little older! Definitely the first three should be good for her, the others might need to wait a year or two depending on her tolerance and what you're okay showing her. But if she watched Little Witch Academia, none of these shows get darker than that, for sure.
Spy x Family - there is some light spoiler 1 in the beginning
Pokemon
Dr. Stone - Profanity/Partial Nudity non-gratuitous spoiler 2 (my 9 yr old loves this show)
Avatar: The Last Airbender
The Legend of Korra - LGBTQ Themes spoiler 3
1
murdering
2
"ass," "hell," "d--k," "s--t"/ backsides, cleavage, revealing outfits, characters imagine each other in sexualized poses (but without sexual activity)
3
Korra is bi-sexual
Movies
My Neighbor Totoro
Ponyo
Spirited Away - illicit substances and blood spoiler 1
Kiki's Delivery Service - smoking
1
There are references to smoking and the drinking of sake. In one scene, a dragon trying to protect the main character is attacked and returns injured and bleeding from the mouth
i suggest Bofuri: maxing out my defense so i dont get hurt. It has some fighting scenes because it is in an vr mmo rpg. But very funny. Dont know about translation tho
Right, yes, I forgot to mention, we watched My Neighbor Totoro & Kiki's Delivery Service. I should probably try to show her some other ones. Good call!
I remember that I loved Spirited Away a lot when I was that age. Some kids think it's scary, but for me it had just the right amount of tension and adventure. (I still like to rewatch it)
Majo no Tabitabi. A very enjoyable magical adventure. Episode 8 has a jump scare that she might not like, so skip that one or watch it yourself first and decide. The episode itself starts with a warning about this so you don't need to remember which one it is.
Somali – another magical adventure, I don't recall it containing any scenes that a child would be uncomfortable with.
Another vote for Bocchi the Rock, it's an awesome and inpsiring anime. Plus, I think it could be empowering to a little girl to see an all girl cast kick ass at being rockstars.
The only con I can think of are a few adult gags, though they aren't super offensive. Most kids shows I watched growing up had adult humor that flew over my head, so it should be fine. Just something to consider.
While I absolutely love the show, I don't think it's a good fit. OP said nothing too dark and the show literally starts with the protagonists willingly selling herself to slavery. It does get more lighthearted from there, but then it gets dark again when the antagonist is introduced.