If she is under 16, then many firms would find it difficult to supervise work experience which was not done in the usual way through the school, as there are lots of laws involved. And, if she doesn't have a "slot" in the year to do work experience, then I don't think the school would let her take time off her classes to do it.
What age is she now? She might be better trying to do something in the summer holidays, and after she's 16 would be easier for firms to deal with.
You would have to contact individual practising psychologists and find whether any would be prepared to take someone on for work experience. There would be issues relating to client confidentiality etc so might not be easy to find someone. In fact, if she was not sitting in on sessions, what would be left would tend to be standard admin matters. BTW there are thousands of girls (far more than boys) at present who want to do psychology and there are very few jobs.
Since she'd probs not be allowed to sit in, I don't think work experience at a psychologists would necessarily be useful at all.
What about working/helping-out for a charity that deals with mental illnesses? They'd probably have somewhere they could put her for free where she'd get an idea of what her potential clients might be like/the stress of knowing other people secrets etc!