。
She took care of the child.
Literal
She [topic-は] that child [genitive-の] care [object-を] did.
世話をする — the standard idiom for caregiving — has a slightly impersonal, dutiful tone; the near-synonym 面倒を見る ('look after,' lit. 'see to the trouble of') sounds more attentive and hands-on. The の linking 子 to 世話 is the typical possessive/relational use: 'the child's care.' Beyond children, the same pattern extends to projects, pets, or any responsibility one assumes — including the polite phrase お世話になる ('to be in someone's care, to be indebted to').