This post-apocalyptic tale of a girl with telepathy and a few other odds and ends in the way of psychic powers, reminds me powerfully of Dawn Cook's _First Truth_ and _Hidden Truth_. Which is backwards, of course, given when they were written. Carmody is Australian, and these were apparently massively popular in the 1980s but didn't see publication in the US until substantially later.
If you like the sent-off-to-Boarding-School-to-be-tormented kind of book, this should do it for you. It doesn't really do it for me. I'm trying to decide how curious I am about the unresolved threads. Like a lot of YA of this type, it does not have enough of a sense of humor for my tastes and has way too much angst and gothic foreboding. Also, the magical cat is slightly cliched.
I realize that in order to have a young character get out and about to see the world you pretty much have to off their parents and have them ostracized by everyone around them and sent somewhere else where they Are Not Loved. And to make it a Tale Worth Telling, you then have to make them some kind of messianic figure. But while I recognize the requirements of the genre, I still find them unbelievably annoying. You probably should know that other people like this book/series/author a lot. You should also know that it's projected to be a 6 book series, the last of which is not yet out, and only the first three of which appear to be readily available in the US.