We do payroll for our nanny ourselves, however my spouse is a CPA so perhaps that makes things easier!
In our state, we need to register as a household employer and file monthly taxes. This can be somewhat tricky -- I've seen many small businesses mess it up. That being said, it is totally DIYable. I'd definitely look into your state requirements in addition to the federal. Look for "Department of Taxation and Revenue" or even possibly "Department of Labor" for guidance. You will also, of course, have to adhere to your state's wage and hour laws.