Yes, she is entitled to holiday pay. The amount of holiday pay she is entitled to will depend on your contract but in the absence of any specific terms the default position is that set out within the Working Time Regulations. Employees have an entitlement to paid annual leave under statute of 28 days per year pro rata which is the equivalent of 5.6 weeks. There is no longer any minimum qualification period for employees to receive this entitlement.
Employees don’t have to have actually accrued the right to this leave before they take it and normally the recovery of any leave taken over and above the amount they would have accrued would have to be specified within the contract. However, the first year of employment is treated differently and you have the right to recover any overtaken leave.
In your case it would appear that, counting the week of holiday which she overlapped with notice, your employee was employed by you for 15 weeks. She has, therefore, in that time accrued the right to approximately 1.62 weeks or 27.5 hours paid leave. From that entitlement you need to remove any days paid leave that she has already had, including payment for public and bank holidays.
If she has insufficient entitlement to cover this holiday then you only have to pay her for the amount she has accrued. If she has more than this amount then you have to pay her for this period of leave and for the remaining accrued but untaken amount.
See also: Holiday pay for laid of workers