Why does Song need Chin to acquire a baby for her? What kind of baby does it need to be?

Song needs a baby to "clinch the deal" with Gallimard. Song knows she is very very close to obtaining Gallimard's complete devotion. Having a baby, specifically a baby boy (Gallimard has now established his masculinity and needs a son to pass it on to), would guarantee her hold over Gallimard and in turn get what intelligence she needs.