I'm guessing someone else in her family has income that's reported (but low enough to still get Medicaid, and EIC). My babysitter asked me for a letter of employment for Medicaid, so you've got to be making something, or supported somehow, to be getting Medicaid. What you're giving her in cash, probably goes straight into her pocket.
Separate question for the tax experts: Is filing a 1099-MISC, that one get's from a company or individual, the same as self-employment? Does there need to proof of the jobs done, besides the 1099?