The federal tax liability seems correct assuming she's filing Single. Without knowing the state, I'm unsure if the state liability makes sense. There are no special tax rates for students, so she'd be taxed the same as any other taxpayer with the same amount of income.
To qualify for the credit, she'd need to have $4,000 in educational expenses that aren't covered by tax free scholarships. If you add an additional $4,000 of scholarship income to your daughter's taxable income, you will be able to take the credit since you meet the income requirements. It will be the same effect as if she received the money and paid out of pocket herself.
