The story
From whelp (“of a canid, to give birth”, verb) + day, by analogy with birthday (“the anniversary of the day on which someone is born”).
Etymology from Wiktionary, CC BY-SA 4.0.
Today it means: The birthday of a canid, especially a dog, or (furry fandom) a furry's canid fursona, typically a dog or a wolf. Full definition →
From whelp (“of a canid, to give birth”, verb) + day, by analogy with birthday (“the anniversary of the day on which someone is born”).
Etymology from Wiktionary, CC BY-SA 4.0.