"How much income can she make before she is taxed at my rate for federal?"
As long as the child's income is earned income like baby sitting and yard work, none of it is taxed at the parent's tax rate, no matter how much she makes. The $6400 threshold (actually $6350 for 2017) refers to when she will start paying any income tax.
Only if she has investment income (interest dividends, capital gains) will some of her income be taxed at the parent's tax rate. Investment income over $2100* is subject to the so called "kiddie tax" (income taxed at the parent's rate).
*Filing a Kiddie tax form (form 8615)is required with only $1050 of investment income, even though the kiddie tax doesn't kick in until $2100.
