The song which plays when the rabbi doll is moved so Rory can get pizza money.
Hava Nagila is a modern Jewish folk song traditionally sung at Jewish celebrations. It was composed in 1918 to celebrate the Balfour Declaration and the British victory over the Ottomans in 1917; there are competing claims over who wrote the simple lyrics, but the tune is a traditional Hasidic religious song. Hava Nagila translates as “Let us rejoice”, and the song is all about being happy.
Notice that the photo from Rory’s sixteenth birthday party is across from the rabbi doll with nodding head, and just behind it is the monkey lamp that Lorelai swapped for Baccarat candlesticks she received as a gift from Emily.