WordNet records no synonym and no antonym for pet sitting. It is the only member of its synset, 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 work of a pet sitter; caring for pets in their own home while their owners are away from home
Synonyms, antonyms and the broader and narrower relations for pet sitting come from Princeton University’s WordNet. Full sources and licences.