Sam Phillips was the composer for Gilmore Girls (she’s the voice of the “la la” filler that runs throughout the series). But Phillips says that she wasn’t the one who chose her song for a pivotal point in the series, that was creator Amy Sherman-Palidno’s choice.
But it’s a perfect choice for the scene in question and it comes back a few other times in the series. I probably would have liked this song anyway, had I encountered it outside the series, but it will probably always elicit an “awwww” because of the way it was used in the series.