You may be over thinking this. She earned that income herself and not as your employee.
You would complete Sch C since the income reflects your tax ID. Report the income and the enter the same amount as an expense as “pass through to….(child’s name aSSN). That will take care of your not paying tax on the income but satisfying reporting it to the IRS.
Then file a Sch C for your daughter reporting the income as cash income. Yes, she will pay some self employment tax. The amount is small enough that she doesn’t have to pay estimated tax. Then just give her the $800 as a gift which would have no tax implications.
