Yeah, Space Cadet would be another good one to get my niece. The author who most shaped my youth was Tolkien, but since I'm not allowed to give them Tolkien, I figured Heilein would suit just fine.
I don't see my brother & family but maybe once or twice a year. It would be really cool if I got to see this niece more often and talk with her as she reads these books. I think I'd enjoy it almost as much as she's going to!
(Hi WN! Hope you've been keeping well. We miss you...)
A book suggestion for your niece: "Ender's Game" by Orson Scott Card. If she's smart and alienated, she will love that book, and she's at about the right age. That and some Heinleins should be enough to make her quite dangerous, later in life - she might end up an engineer or a programmer or an astronaut, you know...