I'd argue that even in a pre-Dominion War Starfleet where ships from big to small (Enterprise-D
to Sisko's Saratoga)
appear to allow civilians and presumably therefore pets, some missions
do not, like Voyager'
s initial mission. From Janeway's discussion with her fiance, I don't think she believed her mission would be a very long one. (It might also be worth keeping in mind that the mission to the Badlands was of a rather tactical and perhaps somewhat dangerous nature.)
Had it been a longer mission, and/or of a less dangerous nature, perhaps both her fiance and dog could have come aboard.