You can only claim your daughter's education expenses if you claim her as a dependent.
If you do not see her name in the education questionnaire, this is because on your tax return she is not your dependent.
In this case, if your daughter files her own return, she only can claim her education expenses, even if you paid for them.
The following is an extract of an IRS document:
Who can claim a dependent's education expenses.
If a student is claimed as a dependent on another person's tax
return, all qualified education expenses of the student are treated as having
been paid by that person. Therefore, only that person can claim an education
credit for the student. If a student is not claimed as a dependent on another
person's tax return, only the student can claim a credit.