Unfortunately the article doesnt give the grounds on which she is appealing.
As to whether she should allowed to be, that is a matter for a single judge who with either grant permission to appeal or deny her permission. If permission is denied, that's more or less it. If permission is granted, then it will still have to be heard by the Court of Appeal and there are no guarantees.
Should she be allowed to appeal? In my view it is fundamental to our justice system to allow anyone who feels aggrieved to make an application for permission to appeal. Whether it should be successful or not really depends on the grounds (although for what it is worth, I do think she is being rather stupid).