Sailing downwind can require more attention and caution to avoid the accidental gybe you describe from occurring.. however, while sailing upwind relies on sailshape and trim for lift and drive, downwind you're primarily looking to create maximum drag.. this means making your sails as "big" to the breeze as possible. That means main sheet and boom fully out, and the jib "winged" out (with a whisker pole if you have it).
This can be uncomfortable esp in sloppy conditions, but it will be fast in a breeze. You do need to pay attention and avoid slewing the boat into a gybe.
Alternatively you can set yourself up on a broad reach (wind coming over the quarter) and gybe back and forth to get downwind much as you tack back and forth to get upwind. You'll sail more distance but won't be so close to an accidental gybe, you'll have a little more apparent wind and the boat will "feel" better. It just may take you a bit longer to get there (or not, depending on wind strength, sailing angles and the type of boat you're on)
1984 Fast/Nicholson 345 "FastForward"
".. there is much you could do at sea with common sense.. and very little you could do without it.."
Capt G E Ericson (from "The Cruel Sea" by Nicholas Monsarrat)