Reddit mentions of Dance of the Photons: From Einstein to Quantum Teleportation

Can I suggest this book? Honestly, I'm not sure what's an appropriate level for a nine year old but it's a bit much I'm sure you can help her out. The book is targeted at the general public and does quite a nice job explaining some of the "sexier" bits of quantum mechanics like entanglement. The author is a very serious and active researcher in the field so you're not getting some half-baked attempt by a non-scientist either.

Ok, looked at this thing (PDF warning) and it looks like a modern physics course + intro mechanics.

If you're interested in more pop-sci stuff I would look into Dance Of The Photons by Zeilinger. It covers some more popular elements of quantum in a very accessible but not crank-y way. Zeilinger is a legit dude. Unfortunately I don't know much about pop-sci physics books because I tend to avoid them.

If you're more interested in textbook stuff, I would look into some of the classic undergraduate books depending on what you're interested in. So stuff like Taylor for mechanics, Griffiths for E&M, and so on.

Of course there's always the Feynman lectures as well which are online. I think all of these should be approachable to you. I'm not sure what your math background is, assuming you're comfortable with calculus and some differential equations. Probably linear algebra as well. If not, I would look into these as well, unfortunately I don't have any book recommendations for these subjects though.

Also did some googling and I found this list which might be handy to look at.