This is just a guess, but do you have enough stuff collected that the dowsing rod is possibly now on the second page of your inventory? Your feather would move there, too, if you gathered enough other stuff.
The feather serves only two purposes, both of which you probably don't need. One is for you to use your Clarivoyance on the feather to see a scavenger hunt item that's high up on a rock in the GPC (the crow that lost the feather is sitting on a rock overlooking the scavenger hunt item so you see the item through the crow's eyes). The other purpose is to let you know that you can use your Clarivoyance on other objects you find in the game (when you open your inventory and you have the power of Clarivoyance, objects you can use the power on will have a faint eye over them). Like I said, you probably don't really need the feather if you really explore every place in the game.