To call Pearl unrealistic is probably an understatement. Pearl is the living Scarlet Letter, the reminder of Hester's failing. She rarely seems like a normal child, often saying things that make no sense for a child of her age. She provides Hawthorne with an interesting way to link Dimmesdale and Pearl, often asking whether he will be with "them" in the light of day rather than in the dark or when they are alone. It's been a long time since I read the novel for the first time, but I suspect that this provides some interesting clues about Dimmesdale when you first experience the book.
Pearl also functions as a counter to the citizens' interpretation of Hester's sin. Despite her symbolic use as the "living letter," sometimes nature is more forgiving than people. In Chapter 16 we read,
Pearl set forth, at a great pace, and, as Hester smiled to perceive, did actually catch the sunshine, and stood laughing in the midst of it, all brightened by its splendor, and scintillating with the vivacity excited by rapid motion. The light lingered about the lonely child, as if glad of such a playmate, until her mother had drawn almost nigh enough to step into the magic circle too.
It's part of Hawthorne's ambiguity that things are not always what they seem; despite her role as the "living" scarlet letter, Pearl has some of Dimmesdale's guilt, and some of Hester's freedom.
The book couldn't be written without Pearl ... or her equivalent. After all, if they committed adultry, how would anyone know without the child? One of the interesting thing to think about is whether Peal was part of one "error" or a continuing pattern of behaviors ... ?