Duplicate stitch is often used to embroider on knitting because it emulates stockinette so well. But there is no reason in the world not to use other embroidery stitches that will give you a rounder circle. Plain old outline stitch comes to mind. Directions here:
If you want to knit the symbol into the fabric of the scarf, you'll have to chart it, using knitter's graph paper, available here:
Then you'll have to learn intarsia, which is not a huge deal. No, you don't have to carry the red yarn all the way up (or down) the black section. You attach it when you're about to start the symbol section, detach it when you've finished the first symbol, and start it again when you're about to do the second symbol. There's a helpful video on this site.
Then again, you could do the whole thing in double knitting, which would give you two super-warm scarves in one: red with black symbols, black with red symbols. But that's a whole other technique.
Oh, and you might enjoy "Knitting for Anarchists," by Anna Zilboorg. One of my favorite knitting books.