It's a 6-year-old kid for God's sake.
Apothecary Diaries -> solving murders is the main theme. Plus prostitution, harems, blackmail, slavery, etc...
Frieren -> slow burn for adults that understand the concept of missed time and looking back. Not to speak about all the atocities done by the demons
The Way of The Househusband -> haven't seen it but a Yakuza themed show ...
Delicious In Dungeon -> sister dies gruesomely and gets turned from a bloody flesh mob into a monster that hunts her own brother and friends.
Sakamoto Days -> I think this one was assassin themed? Not sure.
Romantic Killer -> another assassin-themed show IIRC
Violet Evergarden -> lots and lots of very dark themes, including the war orphan origin of MC.
'Tis Time For Torture, Princess -> nothing wrong with this one, but I don't know how entertaining it would be without knowing what it parodies (torture)
Solo Camping for Two -> adult drama/romance? Why not suggest Yuru Camp instead?
Sugar Apple Fairy Tale -> okay now I know that you are trolling.
Usagi Drop -> aimed at adults. Utterly boring for kids.
Secrets of the Silent Witch -> sure OPs daughter will enjoy MC losing her father due to being burned alive and all the assassination attempts.
With You and the Rain -> another show aimed at adults. The only thing that a 6-year-old would find interesting is that the "dog" is cute.
The Devil is a Part-Timer -> is it really funny to someone who hasn't worked a day in their lives? Plus, again, the theme of dying parents in FMC.