아기를 낳다 (= 출산하다) = to have a baby, to give birth
'Give birth to a baby' is a tautology in English. That said if the emphasis is on the baby sex or type of birth etc. then the 'object' can be added.
여자 아기를 낳다 = To give birth to a baby girl
쌍둥이를 낳다 = To give birth to twins
But, 대리모로 아기를 낳습니다 = To have a baby by surrogacy.