She enters taxable income generated by the 1098-T, whereas you enter qualifying education expenses for the purpose of American Opportunity or Lifetime Learning Credit.
She will claim the excess (and taxable) scholarship income on her tax return no matter what. Because scholarship income is considered to be unearned income, your daughter will be filing Form 8615, because that amount of income will be taxed at your marginal rate instead of her rate. (On the surface, roughly 9,000 of taxable scholarship will be reported on her return).
Now, since she is your dependent, only you can claim any Education Credits (if you choose to do so). However, for you to claim any Education Credits, she will need to claim additional taxable scholarship. (For you to claim 2,500 of American Opportunity Credit, she would need to claim an additional 4,000 of scholarship. You will need to determine if the extra amount she will pay in tax will be worth you being able to claim the AOC, if your income allows you to do so).
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