I think your fungus is actually mealybugs.  Click on the dropdown box for information on how to rid your plant of them: Managing insects on indoor plants | UMN Extension    I do not know exactly which variety of palm you have but here is a link to general directions.  It does not state anything about the root system.  If your plant is only a year old, it should be just fine.  It probably needs to be fertilized.  One clue to when a plant is root bound is water runs right through without keeping the soil moist.  Palmaceae or Palm Family (tamu.edu)