The "-ling" refers to the baby of the animal...mainly birds I think? It's an actual noun, sometimes an adjective, but not a gerund nor continuous verb form.
Duck - duckling
Goose - gosling
Hatchling (ie. the baby which has just hatched out of the egg)
Fledgling (ie. the young bird, about to try flying for the first time)
Compare these with the actual "-ing" forms of related verbs: ducking, goosing, hatching, fledging.
Don't use "fledging"; people will think you mean "fledgling". Even Google asked me that just now.