You need to be clear on what you have: the original Apple Watch didn't have a series number, just names ("Apple Watch", "Apple Watch Sport", "Apple Watch Edition"). When Apple came out with the second generation, they called them "Series 1" and "Series 2". Because of this, many have taken to calling the original ones "Series 0", though this is not official Apple nomenclature.
If you have a Series 1, it's second generation (newer SoC than the Series 0), and watchOS 6 was announced for this back in September. The Series 0 stopped getting updated after watchOS 4. If you can get watchOS 6.1 onto a Series 0, I'll be very surprised.
You're dead right it's a Series O.