If your daughter is under 19 (or under 24 and a full time student) and she does not provide more than half of his own support for the tax year, you can claim her as a dependent.
You do have the choice of not claiming her. If you do not claim her, then you lose the Other dependent credit of $500 and you cannot claim her education credit from his form 1098-T.
As for your daughter, on her own tax return, she is asked the question whether she paid more than half of her living expenses with earned income. If the answer is No, then she must say that she can be claimed as a dependent by someone else.
If someone can claim her as a dependent but does not actually claim her, she can claim the non-refundable part of the American Opportunity credit, but not the refundable part. If she doesn't have any tax liability, then there is no tax benefit for her.
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