I hesitate to recommend a series that I have not read, but I've only heard good things about the Enola Holmes (Sherlock's younger sister) books by Nancy Springer. I have been meaning to read them for some time now, but never seem to get to them.
She may like Eva Ibbotson's books, which often contain a mystery/adventure element. There are several, but I recall DD especially enjoyed The Journey to the River Sea and The Star of Kazan. The reading level might be a little easy for a kid who can manage HP and LOTR, but DD enjoyed reading them into her early teens.
The Westing Game by Ellen Raskin is a good mystery read too.
The Echo Falls mysteries by Peter Abrahams are really good and have a terrific young heroine, but they start off with a murder and may be a little frightening for a sensitive child. I don't think it's too much compared to nazguls, Sauron, killing curses etc. that are present in LOTR and HP. I find, though, that some children seem to tolerate scary stuff in a fantasy novel but not in books with realistic settings.
There's always the really old-fashioned stuff - The Famous Five series and the The Secret Seven series by Enid Blyton. They are filled with problematic gender and racial stereotyping, but I don't think they are much worse than the Nancy Drew books I read at the same age. Somehow I grew up to be a reasonably tolerant, broad-minded feminist.