6-year-old Eiko is more than meets the eye, she is sole survivor of a highly respected race of Summoners and was bought up by a caring group of Moogles. Eiko Carol joins the party immediately, with much the same motivation as Vivi – she does not want to be alone anymore.
Eiko Carol was an interesting change. Sure, she had similarities to other characters (such as Rikku from Final Fantasy X and X-2, and Rydia from Final Fantasy IV), but none were as young and yet powerful as Eiko.
She certainly could be quite trying, very childish and needy, but she is, after all, a child. One of the finer aspects of the game was, in my opinion, her inclusion.