As far as I'm concerned, this looks like a distraction maneuver.

In reality Luna knows, that for the vase that she broke when *storming though the apartment* playing, she is threatened with a disciplinary action in the form of a belt/slipper/rolled up newspaper, so she simply tries to get in good terms with the owner)
Though there are also the drapes, and flowers...and wallpapers...and an extremely important, expensive and unrepairable set of documents that is very important to the owner....
Yeeeesss, it seems that Luna tried to abide with the drawing X)

Or maybe she just wants a puppy =3
Luna definitely inspired by this pic: http://akeahi.deviantart.com/art/Ju.....tion-552288939 =3