I suggest that you let her try it. Tell her that you're willing to try it. Praise her for her willingness to try it but also suggest that you think she's expecting too much of herself. Ask to discuss other ways of doing this that would allow her to keep working for you. I wonder if she's saying she can do it because she wants to stay and is afraid that you'll look for someone else even tho you say you won't.
You don't say how old your children are. I looked at your site. So your children will be 2 preschoolers and 1 toddler. I can't be accurate in knowing ages since I don't know at what date you entered the info. Because all of the children are young, I wonder if you would consider adding a mother's helper for the caretaker. Girls, 11 and 12, on up love to take care of babies and would not expect to be paid very much.
Is she calm and able to manage in stressful situations now? Or is she easily flustered? Is she even tempered without being anxious? She's already caring for 4 very young children. How well is she doing with these 4? Because she's used to dealing with babies already, a newborn may not be too much for her.
If you're pleased with her work, as it sounds like in this post, I would tell her that you will work with her to find a way to make it work. Then, again depending on those variables, I'd let her try it to see if it does work. Allow for time to work out the bugs. The two of you decide on a future date after she starts work with the baby at which you will revisit the question.
Know that it's difficult to find someone to come to your home to care for your children and then more difficult to find someone that fits in with your family. I'd work at finding a way to keep her.