In The Scarlet Letter, is Pearl an unusual child, and if so how is she unusual?

First of all, Pearl in The Scarlet Letter is less a character than a symbol; in fact, it is not until Chapter XXIII that she becomes humanized as she kisses her father, the Reverend Arthur Dimmesdale, who together with her and her mother Hester, stands on the scaffold.

For the most part Pearl is symbolic of her mother's sin and her passionate nature.  Pearl is described as a baffling mixture of strong moods, laughing uncontrollably one moment and sullen at the next.  She has a fierce temper, chasing after the Puritan children who deride her, and holding "the bitterest hatred that can be supposed to rankle in a childish bosom." She described by Governor Bellingham as being like the "children of the Lord of Misrule."  When she is in the forest with her mother, Pearl is capricious, refusing to cross the brook; a "wild and flighty little elf," she will not return to her mother until Hester replaces the scarlet letter upon her bosom.

While Pearl is the embodiment of her mother's beauty and passion, she is also representative of Hester's integrity.  For instance, she pulls away her hand when Dimmesdale refuses to stand with Hester on the scaffold in Chapter XII, complaining, "Thou wast not bold!--thou wast not true!"

Intuitively recognizing hypocrisy, Pearl also senses evil in the same manner.  For example, when she espies Chillingworth in Chapter X, she shrinks from "the black man," exhorting her mother to come away from him because he will harm her.

Very much the soul and spirit of her mother Hester, Pearl appreciates intuitively the beauty of nature. In Chapter XVI, she delights in the play of sunlight upon her and the beauty of the "complaining brook."

While Pearl's strangeness as a character may be attributed to her mental acumen and the abnormal environment in which she is raised, with only her mother as a companion, certainly, there is something other-worldly about her, at least until the events of Chapter XXII bring her completely into the world of humanity.  But, this is the intent of Nathaniel Hawthorne, who utilizes Pearl more as symbol of Hester's sin and waring spirit than as character.  As such, Pearl is one of the most meritable elements of Hawthorne's classic novel.