AFAIK (I am 99.9% certain) she is legally entitled to annual leave and also to be paid for public holidays as these rights are enshrined in Irish statute
In fact, if an employee didn't want to take annual leave and preferred to work instead and get paid for same, they are not allowed to do this as you cannot waive your statutory rights (per conversation with NERA approx 3 months ago)
Is she an employee or an external contractor as a contractor would not be entitled to paid holidays or paid public holidays.