I believe so, except (2) and (3) on your list are actually in identity on further inspection - what God says is good is because God is good - and (1) is poorly phrased - the good is dependent on God at all points, and can not exist independently of him. So invert number (1) and make (3) a footnote to (2) and you’re getting there. I take it you’re studying philosophy and attempting to learn how to make a rigorous argument, distilling your premises down to simple statements so they can be used as major and minor premises in term logic (and, eventually, converted in to predicate calculus). Learning the art of logically-rigorous argumentation - which premises are major, which minor? which premises are presupposed? [to avoid infinite regress] - is harder than arguing well in a rhetorical sense, but you’ll get the hang of it - I know this because the example you give is British-quite good.
Keeping the argument as you have put it has an inconsistency that leaves it open to the assault on the major premise, if good is in any way independent of God, but God knows what is good for us and reveals it, by what law does God reveal it? Couldn’t we learn with our human reason to identify what is good apart from God’s commands given enough time? God forbid! Is the cultural memory of God’s law enough? God forbid!
In ethics, as in all other areas of knowledge and indeed all areas of being, God must be the absolute standard, with no standard existing independently of God, nor any standard dependent on God yet superior to him (as some of the mediaeval via moderna theologians believed in, the potentia ordinata, the ordained power of God, by which God would bind himself to a standard he created. (This is neither here nor there, but reduces to absurdity, and thus the later addition insofar as he deals with men, the concept of pactum.)
(This is a derivative theory that brings in theology proper, i.e. the study of God qua God.) The heart of Divine Command is “the good is the good because God commands it”, without regard for God in himself - why does God command as he does? The why of God commands good is because God is good in himself and acts in accordance with the Divine personality. Two different questions, you see, one asking “Why is a given action moral? Because it is good in itself, or because God commands it?”, and a second question, which is, “Given that the good is good because God commands it, why does God command the good?”
If you wish to be focused, leave out the “why?” (of which my answer is traditional, placing God’s intellect before the will, but there are voluntarist answers that root the “why?” in purely volitional terms, leaving God’s nature out of it), as that’s a paper for another day, or add it as an excursus or put it in footnotes.