There is also a big demand for whole porcelets and suckling pigs, for the same reason.
mid-15c., "an infant at the breast," from suck + diminutive suffix -ling. Cf. Middle Dutch sogeling, Dutch zuigeling, German Säugling. Meaning "act of breast-feeding" is attested from 1799.
c.1400, perhaps a causative form of Middle English suken "to suck" (see suck), or a back-formation from suckling (though this word is attested only from mid-15c.). Related: Suckled; suckling.