I'll try to keep this part short. I assume your child is not married and has no children and nobody other than you can claim her as a dependent. Because you didn't mention scholarships, I will assume scholarships are not significant to this situation. (Your case is simple if my assumptions are OK. But if you have scholarships, then it can be a little more complicated. )
First, if your child has $3000 for her income, then it would be common for the employer to have withheld some amount of money for federal or state tax. Therefore, your child should file her own return to get a refund for any withholdings. If $3000 is her total income, she will file Single, and there should be no tax with that income level. When your child completes her return, she files Single, and she needs to mark her return to note that she can be claimed as a dependent on someone else's return. That is not a choice. She must mark it that way because you "can" claim her as a dependent. [You do have a choice to not claim her (however, then nobody claims her), but that choice makes no sense for you.] And forget talk about Earned Income Credit because it does not apply for her at any income level because without a child, the age for EITC must be at least age 25 and under 65. Quit thinking about EITC for her. Her job is to get her education.
Finally for your own return, your child should remain your dependent. (I am assuming nobody else provides over half of her support). If you otherwise qualify for Head of Household, then file that way. As Head of Household, you get an $18000 standard deduction instead of the $12000 for filing Single. Finally, please become familiar with the American Opportunities Tax Credit (AOTC) for her education. If AOTC applies, then that credit goes on your tax return when she is your dependent, and that credit might get you as much as an additional $2500 of extra refund. You will need your daughter's 1098-T, her school financial statement (to know in which years things get paid), and records for applicable expenses. TurboTax should walk you through the steps. Read questions carefully.
