I can find nothing in the Bible that supports that, but neither can I find anything that opposes it.
Animals are not moral agents, however. I don't know, but I can always hope..
God-consciousness effects worship, which is an activity peculiar to man. But while animals do not have the responsibility of knowing and obeying God, and thus cannot be culpable for sins toward God, such as idolatry, I do believe that dogs at least can experience guilt due to being made that they have disobeyed their master. Which testifies to some degree of conscience and moral culpability toward their masters/law givers.
But lacking the blessing of knowing their eternal creator and His moral will on earth means that whatever punishment they incur for disobeying their earthly master is restricted to this life.