I don't have any experience with this, but I don't think you need to double. Depending on what you've been paying, maybe add a few bucks per hour or even 1.5x what you were paying her, but doubling seems like too much. Do you have any local moms you can ask? Babysitting rates can vary greatly by region.
Faith, 3Aish redhead
Mama to two wild superheroes and a curly-headed baby boy