WordNet records no synonym and no antonym for sturdiness. It is the only member of each of its synsets, which is common for technical, taxonomic and single-sense vocabulary — there is no other English word that means the same thing. The broader and narrower terms below are the useful relations in that case.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
the state of being vigorous and robust
the property of something that is strongly built
resoluteness evidenced by strength of character
“sturdiness of moral principle”
Synonyms, antonyms and the broader and narrower relations for sturdiness come from Princeton University’s WordNet. Full sources and licences.