She is your tax dependent if she is a full-time student and you pay for "more than half" of her living expenses to include tuition, housing, medical insurance and other expenses, and all other ordinary living expenses.
As your dependent you are entitled to a credit for other dependents and also to deduct her tuition and fees expense or to take any education credits, if your income makes you eligible for these credits. The ability to take these credits is very limited for the student (and the refundable portion of the credit is not available to students whose parents are still living.)
If your daughter meets the qualifications as your dependent, you are not required to claim her but she is not eligible for an economic impact payment if she is a dependent or eligible to be one, whether or not you exercise the right to claim her.
If she will graduate in 2020, she will be eligible for the payment, however, when she files her 2020 tax return and will receive it as a refundable credit on that tax return.
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