I've had three Hawaiian feather dusters for over 2 years. The largest one died a couple of weeks ago, so now I'm down to two. I've moved them on occasion since they were located in a deep sand bed. As long as they aren't attached to anything, you can safely move them as long as you are very gentle and very careful not to crush the tube as this will kill the worm inside. I usually dig out a trough, lay the base of the tube in it, then cover it. These dusters occasionally cast their radioles (feathery crown), so if you don't see it for a week or two, DO NOT throw it away. After a week or so, you should start to see short strands of it's new radiole starting to protrude from the tube. They're filter feeders, so it's a good idea to feed them once in awhile. I feed mine once every week or two with a blend of Marine Snow and Phytoplex. I use a turkey baster to spot feed them, and I have to dust them lightly. If the stream is too hard, they'll retract into the tube and the food will float away.
I would move them if I wasn't happy with their location, but that's just me. If you're okay with it stuck in a rock, then you should leave them there. I just wanted to let you know that as long as you aren't too rough with them, they can be relocated. If you attempt it, don't be surprised if it opens up while you're moving it. I think they just want to see what's going on... lol!
