Alongside macOS 10.15.1 comes an update to the Apple Watch as watchOS 6.1. It too supports AirPods Pro.
watchOS 6.1 Release Notes
If you already have watchOS 6 you can update directly from your watch by going to Settings > General > Software Update. If you have an older version of watchOS you’ll have to update from your iPhone. Open the Watch app, tap My Watch > General > Software Update.
watchOS 6.1 introduces support for AirPods Pro and includes improvements and bug fixes. This update also brings watchOS 6 to Apple Watch Series 1 and Series 2.