No, it's not a completely different question; it's the question that underlies this dilemma. Asking what is the "good" and giving the answer as "God", leads to clarifying why God is good and what is "good".
Jack: That was a good action
Jill: Why was it good?
Jack: Because God commanded it and God is good.
Jill: God = Good or God is good?
If we are trying to decide on the source, or fountainhead, of morality, the understanding of what we mean by morality is intrinsic to the very problem at hand. Thou shalt not skill is not just a command; it is a moral command on what is good and evil. But what makes it moral is that it comes from God, and God is the source of morality. And then we get to the dilemma.
I am not sure which way you are going with the word "nature". You seem to want to say that God = Good, that it is his very being. But then you say "it's in God's nature" as well, which is like saying it's a characteristic of God. It is in my nature to get frustrated but it is not the nature of my being. If you mean it is a characteristic of God to be good and to only do good, fair enough, but then good doesn't flow from God, its an independent attribute. So then God hasn't decided on what is good , something else must define this characteristic for God to have it.
Now, if God made the rules based on his very essence, we are still left in a bind. Once again we are forced to ask how we define "good" and "evil". God's commands tell us what is good and evil. And how does God decide what is good and evil? God = Good. So saying something is "good" is really just saying it's "God" with an extra "o".
Being constant doesn't change the fact that the origin of "good" is what we are after. He can stick to his guns all he wants but we still need to know where the definition of the "good" arises. Because if the answer is simply "God is good", we still need to answer why.