If she has been working for you did just 6 months, she wouldn't be able to claim Unfair dismissal. If you really want to let her go, then I suggest you make her an offer ... You probably can't expect her to happily work her notice. In fairness, you should probably pay her for outstanding leave and for her notice period, and possibly a bit more. It might help to agree a reference with her, too. It should be possible to deal with this in a fair and reasonable way, but if she really has no idea you are so unhappy, it is sure to be a bit of a shock.