Her refund is small because she is being claimed as a dependent.

Dependents only qualify for a 6,300 standard deduction and they do not get an exemption. Therefore your daughter is paying tax on 2,400 dollars (8,700-6,300 = 2,400). The tax rate is 10% or 240 dollars. The refund would be 82 dollars (or 83 depending on rounding differences).

If she claimed herself, she would get the 6,300 dollars standard deduction and a 4,050 dollar exemption. She would not have any tax, and would get the entire 322 dollars of withheld tax as a refund.