I know what you're talking about, but since the Animal Crossing series has a track-record of not having an official soundtrack, people usually rip the music.
I did a quick YouTube search when I saw this thread last night. I couldn't find anything, which isn't surprising since it's only about a minute long, only plays at that one point in the game and doesn't really have a specific title.
I think the easiest thing to do would be to rip it yourself, or record it from your game. Since it takes less than five minutes to get to that point in the game, you could always just play up until the music plays, then leave your 3DS going to listen to it?