The Spiderwick Chronicles by Tony DiTerlizzi and Holly Black
The Goosebumps series by R.L.Stine and the Babysitters Club series by Ann M. Martin were really popular in the 90’s
Percy Jackson and the Olympians series - Rick Riordan
Tollkien’s The Hobbit (and if she really, really likes it, maybe the Lord of the Rings)
My niece and nephew are currently raving about the Warriors series, by Erin Hunter. They’re not quite so enchanted with her current series, Seekers, but they are reading them. (She’s almost 14, he’s 10).
Ursula LeGuin’s Earthsea stories (A Wizard of Earthsea, The Tombs of Atuan, The Farthest Shore, Tehanu, The Other Wind, Tales from Earthsea)
Anne McCaffrey’s Dragonriders of Pern - especially the first trilogy (Dragonflight, Dragonquest, and The White Dragon) and the Harper Hall trilogy (Dragonsinger, Dragonsong, and Dragondrums)
Any of those should be suitable for a 13 year old. And I’d say have her give Harry Potter another try. He’s 12 at the start of the first book, and they are very well written, and are intended as juveniles.
When she’s a bit older, you might also consider:
Tanya Huff’s “Blood” series, if she likes vampires specifically (Vicki Chase and Henry Fitzroy), with kind of a mystery element to each novel (some minor sexual tension, but nothing really explicit)
Glen Cook’s Garret P.I. stories
Hope that helps