RORY: How much older could [Paul] possibly look?
LORELAI: A lot! He’s usually a little scruffy, and then the baseball cap hides the funky hair thing.
RORY: He should’ve been holding a yo-yo and a lollipop and wearing a beanie with a propeller on it.
Rory is describing a stereotypical little boy as depicted by cartoonists in the 1960s and ’70s in particular, although it’s never quite gone away.
The helicopter beanie comes from the 1962 animated television show Beany and Cecil, based on the puppet show Time For Beany (1949-1955). Beany was a cherubic-faced blonde boy who wore a cap with a propeller on it that allowed him to fly, and as a result, similar caps became popular marketing novelties. Beany and Cecil had a revival in 1988, The New Adventures of Beany and Cecil, by the same people who made Ren and Stimpy.
Rory and the rest of the town tease Lorelai mercilessly for dating someone who is, at most, ten years younger than she is. Fans often say they wouldn’t have teased her for dating someone ten years older, which I think is correct, except in the case of Luke. He told her Ian Jack, the Chilton dad, was “too old” for her, and the actor playing him is ten years older than the age Lorelai is supposed to be. As Luke never even saw Ian, I’m pretty sure he would have objected to him whatever his age!