Which character is "perfect love"?
The 'Arabian Nights' -- or more correctly, the ''Alif Laylah wa'al Laylah'' (The One Thousand and One Nights), is not properly a book in the sense of books today, but more a book-collection of various stories from the Middle East, South Asia, Central Asia and so on, collected and adapted and told many times over the centuries since Islamic medieval times, and still quite popular in these parts.
While there are many characters within the many stories in the collection, men and women, who could be possibly labeled 'perfect love', I believe that you are essentially asking about the frame story i.e. story in which the other 'stories' spread out over 1001 nights, are told. I am sure you are familiar with this-- Sheheryar the cruel king, who weds and sleeps with a new wife each night and has her slain each morning, is married by the Vizier's wise daughter Scheherazade, who, with her loving ways and by cleverly telling the fickle king a new story each night for a thousand and one nights, wins his love and affection and is thus herself saved and saves many other maidens too, in the bargain, who else would have also falen to the king's whims.
As such Queen Scheherazade's 'scheme'and her self-sacrifice, in taking up the king's challenge and marrying such a creature; and her ultimately winning him over and 'taming' him into some human semblance, is indeed an act of great courage and selfless love-- for the people, especially the young women of the kingdom and for the poor ego-centric king too; and for all humanity.