The Mixed Up Files of Mrs. Basil E. Frankweiler by E.L. Konigsburg is a classic mystery for young readers.
Pure Dead Wicked by Deb Gliori (and a bunch of sequels) is fun, with more yucky gross out stuff than creepy, scary stuff, about a sort-of Addams Family in a crumbling mansion in Scotland.
I haven't got around to reading the Enola Holmes (Sherlock's younger sister) series by Nancy Springer yet, so I don't know how scary it is, but the mysteries are supposed to be quite good.
The Mysterious Benedict Society by Trenton Lee Stewart
The Name of this Book is Secret by Pseudonymous Bosch
The Echo Falls mystery trilogy by Peter Abrahams - the first book starts with a murder and it put DD right off the entire series, which is too bad, because they are well written. They may not suit your DD now, but may in a couple of years if she still likes the mystery genre. I think if a child can read about all the torture, murder and mayhem in Harry Potter, they'll do fine with this series.