I was wondering before if it would count as a planet if it wasn't bound to Earth. It is around 6 times more massive than Pluto. There are also other, bigger moons in our solar system, such as Ganymede, which has about half the mass of Mercury (but also has a bigger diameter, due to being significantly less dense).
One could defend the Earth-Moon system to be a double planet. The Moon is much too large compared to other satellites in the solar system.