Yes, they're a kind of worm, Annelids, IIRC. Be prepared for all
kinds of "icky" things since you've taken on a saltwater system, par for the course,
mom.
My experience has been that, much like when a bird's feathers get all whacked looking and they must molt them, featherdusters will eventually shed their crowns. However, if you're really new, and the system is really new, other issues need to be addressed first: water quality being the foremost. Being invertebrates, they'll be more sensitive to salinity changes, as well as certain compounds--namely ammonia and nitrite, although high nitrate levels will affect them adversely as well.
So, assuming you've got proper salinity, pH, and zero readings on the above, we might come to the conclusion that its feathers were simply thrashed and it's time to grow a new crown. I have had best luck target feeding them (phytoplankton or similar foods intended for filter
feeders) to encourage growth of that new crown ASAP. It should also be attempting to cover itself with grains of substrate, assuming it's not so large that it can't "grab hold" of the stuff with its exudations, if it's not already building itself a new tube.
If in doubt, do a water change! (But I wouldn't recommend vacuuming the substrate at this point.)