Do you specifically want her to be reading classic adult literature? If she liked Farenheit 451, she could try some of Bradbury's other books, he's pretty accessible (though the rest of his work is not generally considered classic outside of SF). If she likes speculative fiction, some other authors who are generally considered classic in their field and also write in a fairly modern style are Peter S. Beagle (THE LAST UNICORN is an amazing book), John Wyndham (THE MIDWICH CUCKOOS, THE KRAKEN WAKES), Kurt Vonnegut (SLAUGHTERHOUSE-FIVE, CAT'S CRADLE), and H. G. Wells (THE ISLAND OF DR MOREAU, WAR OF THE WORLDS). If you want more literary classics, I enjoyed Dickens's A TALE OF TWO CITIES as a teen, as well as THE GREAT GATSBY (Fitzgerald), CATCH-22 (Heller), and some of Hemingway's work (THE OLD MAN AND THE SEA, THE SUN ALSO RISES).
On the other hand, if she's just interested it trying some adult books in general, I'd say go to the library and look for books in the genres she enjoys in YA. I loved fantasy, science fiction, and the supernatural as a kid and teen, so it's not surprising that the first adult books I gravitated toward were Anne McCaffrey's work and Stephen King's. After I started reading them, I'd just browse the SF & Fantasy section at the library, reading book descriptions and seeing what sounded interesting. You could also check if her favourite YA authors have written adult books as well (many have), which could be a good starting point.