As someone who has watched anime for decades, I personally do not recommend letting anyone under high school age (and even then…) watch any anime that you have not fully watched and vetted yourself. Anime is notorious for pulling a fast one on the audience and doing a sudden genre/maturity shift (from Narutaru which looks like a cute Digimon-type monster battle show but involves a lot of murder and rape, to School Days which looks like a standard high-school romantic drama but ends with the protagonist’s head in a duffle bag). These “gotcha!” moments are part of what makes anime unique and fun, however it also makes vetting anime really difficult for guardians. And that’s just in terms of violence; anime often feature (what I consider) really unhealthy portrayals of romantic relationships, female sexualization, and sexual harassment in general (the latter of which often is played off as a harmless joke). Even “kids” anime like Naruto, DBZ, etc can be surprisingly mature. You have to pay very close attention to the show’s rating, but even that is highly subjective and can change from season to season or even episode to episode, and often doesn’t include factors like “does this series promote toxic relationships?” that are important but often overlooked when vetting media for such a developmentally-vulnerable age.

There definitely are anime out there that are appropriate for younger audiences, but your daughter might find them boring and dated by comparison (anime fandom nowadays is all about watching the latest hot series, not digging years or decades into back catalogues for shows that have completed and thus easy to confirm are age-appropriate to the end). Generally, slice-of-life CAN be wholesome (eg Non Non Biyori or The Flying Witch) but your daughter may find them boring. There are also more appropriate action series out there, but you gotta find the stuff that’s aimed for really young kids like Digimon. Magical girl anime is also an option (some ancient examples: Sailor Moon, Saint Tail, Kamikaze Kaitou Jeanne), but that’s a popular “gotcha” genre so you have to be VERY careful.

In summary, having a kid who’s interested in anime means either having to very carefully vet each title yourself and praying your kid doesn’t gain an independent streak and start exploring titles herself, or giving up and hoping she doesn’t stumble across the animated equivalent to 80s/90s kids stumbling across beheading videos and scat porn in the early days of the Internet. Good luck?

@Pillagenplunder@lemmy.world has the go-to suggestion: you can’t go wrong with giving Avatar: The Last Airbender a shot. I don’t know if I’d say it has similar themes or notes to Demon Slayer but it is an absolute winner.

I also highly recommend the movie Spirited Away if you haven’t watched it together yet. It’s got some similar themes and notes more suitable for the whole family. Instead of stopping demons with violence, Spirited Away finds diplomatic ways to deal with spirits. Also just a masterpiece of a movie.

I’m having trouble thinking of similar anime series for a younger audience but there are some other anime-inspired (like Avatar: TLA) cartoons that deal in similar themes. Steven Universe follows a group of heroes that stop corrupted gem creatures in hopes of curing them. And Star Vs. The Forces of Evil is about a Sailor Moon-like princess from a magic realm that travels to Earth and fights the forces of evil with her best friend trained in karate.

Maybe oldschool Dragon Balls or Rurouni Kenshin? I wonder if Hunter x Hunter or One Piece might be better? I’ve only watched the former a bit and I think it has significantly less graphic violence at least. Alternatively maybe something completely silly like Samurai Pizza Cats.

Avatar:the last Airbender