Luna P was a device used by Chibiusa. It was her dear friend and it bore a strong resemblance to Luna, much to her chargin. In both the manga and anime versions, Luna P seemed to have some self-awareness; it followed Chibiusa and defended her.
With the vocal command "Luna P Henge," it could transform into various objects that would help Chibiusa, such as a parasol that could hypnotise people, or a sleeping potion. It was also used to communicate with Sailor Pluto and the other Senshi.
Black Lady's response to Luna P varied between the anime and manga. In the anime, Black Lady viewed the device as her only true friend, and used it to attack the Sailor Senshi. In the manga, however, Black Lady smacked it away, calling it a stupid toy.
In Act 28 of the manga, Luna P transformed into the Pink Moon Stick when Sailor Chibi Moon desired the power to help her friends.