Your haiku (or is it a senryu?) works for me, Ray Rasmussen – although I would be in me bed earlier than 3am, dog or no dog!
twig in beak
a crow flies over a dog
An all-season ‘mu-ki’ [‘no season’] ‘topic’ [theme] or ‘keyword’ [to link themes] is allowed in Japanese haiku rules. Muki can stand in for a ‘kigo’ [seasonal reference]. Throwing a stick for a dog, like skipping a stone over water, or kite flying, are muki, therefore haiku events [rather than senryu, or zappai].