RORY: I just thought if she saw how we lived, and how pretty it was with the lake and the swans …
LORELAI: That she’d do a happy dance?
In slang terms, a “happy dance” is any spontaneous dance done in celebration, or in order to gloat at personal success.
It’s especially known from the Peanuts cartoons by Charles M. Schulz, where Snoopy does an excited happy dance whenever Charlie Brown brings him food. This may have been part of Lorelai and Chris’ performance when they sang Suppertime, from the musical You’re a Good Man, Charlie Brown.