I assume this sitter will come to your home. She is your employee.
She doesn't provide documentation of her income, you provide that as her employer. You will need to issue her a W-2. That will be proof to the IRS of your payment.
Since she is your employee, you also need to have her fill out Form I-9 (not W-9, not W-10) and provide her proof of eligibility to work (by a photo ID and Social Security Card).
If you pay cash, give her a statement of the time worked, rate of pay, withholding of income and payroll taxes. You keep a copy of the statement. It would be fine to have her sign your copy of the statement before you give her cash.
It would be better to pay her with a paycheck showing all deductions, just like a regular employer.
In addition to claiming a credit for childcare, file Schedule H with your tax return to pay your required withholding of income and payroll taxes.