Tuck Everlasting is a kids' book. Sure, it has some pretty heavy-duty, mature content. But guess what, world? Young readers can handle it.
Less clear-cut is calling it fantasy. In fact, even though most of the main cast of characters is immortal, Natalie Babbitt doesn't think her work is a fantasy: "Well, everybody thinks my books are fantasy, but they're not" (source). Doesn't get more clear than that. But we don't have to agree. Do you?