Thanks for your question.
How long have you employed her and does the employment contract state a specific length of notice period?
Until employees have been employed continuously for one year they generally only able to pursue rights for breaches of contract. She does not have the right not to be unfairly dismissed. You can dismiss her for the reasons you state and provided you have (and will) not breached any terms of her contract then you will face no recourse from the employee.
You are probably bound by the terms contained in the employment contract with respect to notice so I would give her the one month in stated in the contract (the statutory minimum is only one week for future reference), if you do not she may have a claim against you in this regard.
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