Translation:Do you want to be taking care of my child?
Yes, "Do you want to take care of my child" is a more common English formulation, though I wouldn't say that "Do you want to be taking care of my child" is wrong. (The version with "take care" was just accepted for me.)
Perhaps the authors wants to maintain the perfectivity/imperfectivity. In that case your sentence is closer to "postarat", not "starat".