Yes, she must file a tax return, because she has over $6300 of income.
Note that the difference between $10,350 and 6300 is $4050. Because you are claiming her $4050 personal exemption (deduction), on your return, because she is your dependent, she does not get to claim it on her return. She still gets a standard deduction, so any income over $6300 will be taxed and she must file to pay that tax
EDIT. Note: for tax years 2018 and beyond, the $4050 exemption has been eliminated. The Standard deduction has been increased to $12,000. So, a student-dependent with under $12,000 of earned income would not be required to file
