Yes, DADGAD tuning is different. That's why I gave you the chord patterns! Retune to DADGAD (which is a D tuning; you don't use it for any other key) and capo 5, which means you will he playing in G.

Then play in the positions I gave you:

D: 000200 or 004200

G: 020020

A: x0220x or x02242

So the D positions will sound a G, the G positions will sound as C, and the A positions will sound as D.

So this would sound as


         G
Will ye gang tae the Hielands, Lizie Lindsay?
                                  C
Will ye gang tae the Hielands wi' me?
         G
Will ye gang tae the Hielands, Lizie Lindsay?
    C            D          G
My bride and my darlin' tae be?