I don't know if they are passed along or if a new bracelet is made for each person.
I found a picture of Countess Ingrid von Pfeil und Klein-Ellguth (Princess Benedikte's granddaughter) wearing a gold bracelet. It was taken in July 2009 so she would have been five years old.
And some more pictures of Princess Josephine wearing her bracelet at the Danish royal family's annual summer photo session today.