Bear- I have washed & dried pillows as well as down comforters, for years. Also down vests & jackets.
I just wash on cool water, regular soap, could use woolite, if you have it on hand, Do an extra spin cycle. Put in dryer, w/ at least 2 tennis balls, or an old clean tennis shoe. The balls beat the living crap out of the feathers & helps them re fluff. I have hung items on the clothes line to dry than put in dryer just to fluff. If you don't fluff, all the feathers clump in a lump, and refuse to distribute.
Good luck