You do not report your daughter's income on your return.

You can claim her as a dependent.

If her unemployment income is less than $12,400 (the standard deduction), she is not required to file a tax return. However, if she had taxes withheld, she can file a tax return to claim a refund.

At more than $12,400, she has to file her own tax return. .

If she files a tax return, she has to indicate in TurboTax that she can be claimed as a dependent by someone else.

I claimed my daughter as dependent  on my taxes, but when she filed her taxes using turbo tax, her standard deductions went down to $5500 instead of $12,400 as expected. She did receive 16 K unemployment compensation and $5700 in earnings from her other job.  She graduated end of May  from college. Why TurboTax is changing her standard deductions???

The standard deduction for dependents is limited to earned income plus $350, but no greater than the normal standard deduction.  This rule is in place to discourage parents from putting large amounts of investment income in the child's name to avoid taxes.  This is part of what is known as the "Kiddie Tax".   

The unemployment income is "unearned" income for your daughter.  

Here is a link with more information on the standard deduction for dependents.  You can use table 8 in the link to see the calculations.  

If your daughter provided more than 1/2 her own support in 2020 she would not be claimed as a dependent child.  Since she has more than $4300 of gross income so she would also not be a qualifying relative.  The dependent rules would then not apply.

Here are rules for qualifying as a dependent.

Qualifying Child:

1. The child must be your son, daughter, stepchild, foster child, brother, sister, half brother, half sister, stepbrother, stepsister, or a descendant of any of them.

2. The child must be (a) under age 19 at the end of the year and younger than you (or your spouse if filing jointly), (b) under age 24 at the end of the year, a student, and younger than you (or your spouse if filing jointly), or (c) any age if permanently and totally disabled.

3. The child must have lived with you for more than half of the year.

4. The child must not have provided more than half of his or her own support for the year.

5. The child must not be filing a joint return for the year (unless that joint return is filed only to claim a refund of withheld income tax or estimated tax paid).

Qualifying Relative:

1. The person can't be your qualifying child or the qualifying child of any other taxpayer.

2. The person either (a) must be related to you in one of the ways listed under Relatives who don't have to live with you , or (b) must live with you all year as a member of your household (and your relationship must not violate local law).

3. The person's gross income for the year must be less than $4,300.

4. You must provide more than half of the person's total support for the year.