alone, spontaneously, Germany
獨 centers on being the only one: alone, solitary, or acting on one's own. The 'Germany' meaning is a specific application of the 'alone' idea, used in the country's name.
獨 combines 犭 (dog/animal) with 蜀, which likely contributes the sound. The idea of a lone animal may have given rise to the meaning 'alone'.
A single animal 犭 stands apart from the group, represented by the complex shape 蜀. Picture a lone wolf howling by itself: 獨 means alone.
For ドク, imagine a lone doctor (ドクター) treating a solitary animal: doctor -> ドク, and the animal is alone.