Applying the moral argument to God himself

I think there's a question that seldom gets asked from apologists (who advocate the argument from morality):

"Is God a moral being?"

If they advocate the moral argument (ie. the notion that morals somehow exist independent of humans and have been "created" by something) and they answer "yes" to that question, the argument becomes circular. If God is a moral being, then said morality has to, according to their own argument, exist independent of God and have been created by something else.

If God is not a moral being, then how can he even dictate morality to others? Wouldn't morality thus be by definition subjective, something that God came up with?

The whole problem with this entire argument is that it's self-contradictory. The core problem is that it assumes that morals have to somehow been "created" for them to "exist." As if they were some kind of immaterial entities floating out there that something created and can manipulate like they were objects or something.

The actual situation is that morals are simply a function of how living, thinking beings work. A side-effect. An emergent behavior of simple physical laws acting on complex mechanisms. They are not any kind of entities that exist independent of us, floating somewhere out there affecting our brains. They don't have to "be created" by anything.