Yes, that is the kiddie tax. She actually has no "unearned" income.
The most likely explanation is you have entered the 1099-NEC as misc. or other income, rather than as self employment (earned income). You probably entered the$1000 scholarship as other income, rather than scholarship (taxable scholarship is treated as earned income for purposes of the kiddie tax and dependent standard deduction).
As you surmised you do not need to enter the 1098-T, as it was all covered by tax free scholarship (more on that below). You also do not need to enter the $1000 spending scholarship as she can claim it was used for books.
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There is a tax “loophole” available. The student reports all his scholarship, up to the amount needed to claim the American opportunity credit, as income on his return. That way, the parents (or himself, if he is not a dependent) can claim the tuition credit on their return. They can do this because that much tuition was no longer paid by "tax free" scholarship. You cannot do this if the school’s billing statement specifically shows the scholarships being applied to tuition or if the conditions of the grant are that it be used to pay for qualified expenses.
Using an example: Student has $10,000 in box 5 of the 1098-T and $8000 in box 1. At first glance he/she has $2000 of taxable income and nobody can claim the American opportunity credit. But if she reports $6000 as income on her return, the parents can claim $4000 of qualified expenses on their return.
