They can't expel her for having mental health problems, unless it's affecting her work and behaviour in such a way that she does something worthy of expulsion (for example, if she's self-harming in front of others); and even then, they'd have a very tricky time of it. That's not to say that they couldn't get social services/child protection involved though, and that may lead to your friend being removed from school if they feel that it's the wrong place for her.
Also if this "psychologist" is actually threatening her then your friend needs to go above the psychologist's head and report it to someone. That should NOT be happening.
That's about the best advice I can give. I'm at home for Easter atm so luckily enough I was able to ask my Mother, who is a mental health professional; but we're in the UK, not Australia. It might be different over there.