You are liable for tax from the first cent you earn.
However, depending on rate of pay, tax credits and standard rate cut off point, your niece will probably end up paying little or no tax.
For example, in 2005:
Standard Rate cut off point: 29400
Annual Tax Credits: 1580 + 1270 = 2850
PRSI Class: A
This means that she can earn up to €14250 in the year without paying tax or PRSI.