Short answer
Yes, a single, plain, thoroughly cooked oyster is generally safe for a small dog as an occasional tiny treat. The risk isn't about toxicity but about portion size and preparation — a whole oyster is a large mouthful for a 5 kg dog and could be a choking hazard or cause an upset stomach if they're not used to it. Always cook oysters fully to kill bacteria, never feed raw, and chop it into pea-sized pieces. Monitor for any digestive issues afterward.
Oysters — Food safety facts
Safe to share · Dogs · full breakdown on the linked food page
Cooked oysters are safe occasionally. Raw oysters carry Vibrio bacteria.
The full verdict, portion guidance and serving notes are collected on the Oysters food facts page.