This sounds like quite a fun challenge.  I read this and am wondering what she meant when she asked to take on more responsibility.  Can she define what that means to her?  It sounds like she is excited to have a job and wants it 'all' but she may not really understand the role of a PA (which I'm assuming is similiar to an Executive Assistant here in the states).  When I've mentored green assistants in the past I started out with the basics and built on that - if there's nothing else you're comfortable giving her at her level, then she needs to find ways to be productive.  

You may want to suggest some reading materials for her such as Inner Circle Assistant, by Joan Burge (my work bible) and/or the Complete Office Handbook.  I also believe that honesty is the best policy and suggest to her that she focus on her spelling, writing skills, etc.  If you create an open and mutually respectful environment for her, she'll be more comfortable with what you do or don't give her.  She needs to find her own working style so your challenge is to allow her to do that while guiding her to focus on getting her work done efficiently and accurately.