The book is real, and I think we should assume it's one-of-a-kind, like Harry's invisibility cloak or other such artifacts.

From the wikipedia entry for Hogwarts (http://en.wikipedia.org/wiki/Hogwarts):
"A magical quill at Hogwarts detects the birth of wizard children and writes their names into a large parchment book.[13] Every year, a teacher (in recent years, Minerva McGonagall) checks this book and sends a letter to the children who will have turned eleven years old by 31 August."