The standard deduction does not negate the fact that she had self-employment income of $1200 and has to pay self-employment tax for Social Security and Medicare for her self-employment income, since it was not taken out of her pay.
You have not mentioned her age, nor have you said if you claimed her as your dependent, so it is hard to answer you. However with so little income it seems likely that you would be claiming her.
She is a graduate student so is not eligible any more for the American Opportunity Credit. But grad students can use the Lifetime Learning Credit. If she is not being claimed as your dependent, she can enter the education credit on her own return--did she use the Lifetime Learning credit? If she is your dependent the credit goes on your return.
The education credits are not related to her standard deduction. A credit reduces the tax you owe.
She cannot deduct anything for her health insurance since she cannot itemize and enter medical expenses
https://ttlc.intuit.com/questions/3262984-who-is-eligible-for-the-lifetime-learning-credit
The other thing you may not realize about that standard deduction if she is being claimed as your dependent:
For 2019, the standard deduction amount for an individual who may be claimed as a dependent by another taxpayer cannot exceed the greater of $1,100 or the sum of $350 and the individual’s earned income (not to exceed the regular standard deduction amount).
Edited: I took a second look at the amount of tax you say your daughter owes -- are you sure it is not $187 instead of $87? Self employment tax is 15.3%, and you said she made around $1200. $187 would be more like it.
**Disclaimer: Every effort has been made to offer the most correct information possible. The poster disclaims any legal responsibility for the accuracy of the information that is contained in this post.**
