The Hide Dock icon checkbox works on macOS 10.14, but it may not appear so at first due to a change Apple has made to the Dock. In macOS 10.14, there is a new section of the Dock that shows recently launched applications. Applications will show up in this section, even if their Dock icons are hidden (so that they don’t show up in the regular part of the Dock). If you want to hide ToothFairy from the recent section, as well, you can either:

  • Click and hold on the ToothFairy Dock icon and choose Options ‣ Remove from Dock from the menu; or
  • Drag the ToothFairy icon off the Dock; or
  • Go to System Preferences ‣ Dock and uncheck Show recent applications in Dock to hide that section entirely.