why is it meus and not meos?
meus is nominative singular to match with canis here. canis is nominative since it is our subject, what we are talking about, describing.
meos would be accusative plural. If it was an action being done to 'my dogs' then we could see canes meos.
Canis, canis (dog) can also be masculine or feminine; it depends on the dog. https://en.wiktionary.org/wiki/canis#Latin
"Canis mea in culina est" should be accepted, too.
Canis in mensa stat