"a young duck," early 15c., from duck (n.1) + -ling. The ugly duckling is from Hans Christian Andersen's tale (1843 in Danish, by 1846 in English).
Entries linking to duckling
duck n.1
waterfowl, natatorial bird of the family Anatidae, Old English duce (found only in genitive ducan) "a duck," literally "a ducker," presumed to be from Old English *ducan "to duck, dive" (see duck (v.)). Replaced Old English ened as the name for the bird, this being from PIE *aneti-, the root of the "duck" noun in most Indo-European languages.
In the domestic state the females greatly exceed in number, hence duck serves at once as the name of the female and of the race, drake being a specific term of sex. [OED]
As a term of endearment, attested from 1580s (see ducky). duck-walk, a squatting waddle done by a person, in imitation of a duck, is by 1915; duck soup, slang for "anything easily done," is by 1899. Duck's ass haircut is from 1951. Ducks-and-drakes, skipping flat stones on water, is from 1580s; the figurative sense of "throwing something away recklessly" is c. 1600.
-ling
diminutive word-forming element, early 14c., from Old English -ling a nominal suffix (not originally diminutive), from Proto-Germanic *-linga-; attested in historical Germanic languages as a simple suffix, but probably representing a fusion of two suffixes: 1. that represented by English -el (1), as in thimble, handle; and 2. -ing, suffix indicating "person or thing of a specific kind or origin;" in masculine nouns also "son of" (as in farthing, atheling, Old English horing "adulterer, fornicator"), from PIE *-(i)ko- (see -ic).
Both these suffixes had occasional diminutive force, but this was only slightly evident in Old English -ling and its equivalents in Germanic languages except Norse, where it commonly was used as a diminutive suffix, especially in words designating the young of animals (such as gæslingr "gosling"). Thus it is possible that the diminutive use that developed in Middle English is from Old Norse.