Holden talks his sister up to no end. She's the smartest kid ever, he assures us, as well as a great dancer, emotional, and funny. She always knows what you're talking about. She can tell the difference between a good movie and a bad one. She listens.
Then we meet Phoebe. And basically, she's everything Holden said she would be. She's a pretty amazing character because she somehow manages to be all over the above, but still very much ten years old. (Check out her notebook scribblings – they're a ten-year-old's in every way.) We do feel the hand of authorial manipulation when Phoebe corrects Holden about Robert Burns, but hey, it was the forties, so maybe kids just knew that stuff back then.
Still, it's this mingling of child-like enthusiasm and adult-like incisiveness that makes Phoebe so compelling. Her notebook entry has exclamation points (child), but she points out to Holden that, really, he doesn't like anything (adult). She's smart enough to figure out that Holden's gotten the ax again (adult), but responds by putting a pillow over her head and repeating, "Daddy'll kill you" (child). Now what about her wanting to run away with Holden? Child, or adult? Child, sure, because she packs a suitcase thinking stubbornly that she'll go out West somewhere and not come back. No, wait, that's Holden. Phoebe isn't gung-ho to run away, she's gung-go to be with Holden, and it's rather likely that she's doing so because she feels – probably not consciously – that he needs someone to care for him.
When Holden refuses to let her come, she takes care of him in her own way, in that touching carousel scene when she puts his red hunting hat back on his head. Phoebe gives back to Holden, unlike every other character ever (see Holden's character analysis for details).
So, in Holden's eyes, Phoebe is exactly the sort of child he wants to protect by being the catcher in the rye. It's no surprise that she's the one he chooses to tell about his dream. Her reaction ("Daddy's going to kill you") doesn't convey it, but we have a feeling Phoebe knows exactly what Holden's talking about – just as he promised us she would.