Yes, this is excellent. You corrected my mistake in the refrain where I had it going to G, but it goes (as you note) back to D and THEN goes to G in the last bar.
The only difference I could add, now that I heard it again, is that the G modulates to a G7 on the bar before the refrain.
Giving praises to our (G)God (G7).
"Glory to the precious Lamb of (G)God (G7)."
Where there's no sorrow nor (G) pain (G7).
The chords are very simple so finding a suitable key will be as easy as cake. Or pie.