I will assume that your daughter is not married, has no children, and receives her support from you. And because you did not mention scholarships, I will assume that they are not significant for this response in order to keep it as simple as I can.
I assume that her employer withheld some state and federal taxes on the $3000 that she earned and that she has no other income. In order to get her withholdings refunded to her, your daughter should file her own return as Single, and she needs to mark her return 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.
Forget talk about Earned Income Credit. Without children, the age for EITC needs to be 25 and under 65. Her job is to get her education right now.
If you otherwise qualify to file as Head of Household, then file that way. Head of Household gets a $18,000 Standard Deduction compared to only getting $12,000 when filing Single. You file with your daughter as your dependent. If you don't claim her, then nobody get the dependency for her. If she is marked as your dependent, you can then look at claiming the American Opportunities Tax Credit (AOTC). That credit has the potential to increase your refund by as much as $2500. You will need your daughter's 1098-T from her school, her school financial statements (to know in which years money is paid for items), and records of applicable expenses such as tuition and books.
