RORY (reading from card): “Buttercup is a special dog. She’s extremely skittish and tends to react badly towards blonde haired females, brunet males, children of either sex, other animals, red clothing, cabbage, or anyone in a uniform.”
LORELAI: (to Luke) Hey, we just found the doggy version of you.
Naturally Lorelai would be attracted to a dog version of Luke – who is of course doggedly loyal to Lorelai.
The dog Lorelai eventually gets is even more neurotic and weird than Buttercup.