I have my daughters (6y/o) little guitar tuned in an open Gmaj tuning, and I teach her melodies on the g string...like insy winsy spider, and then show her how to use a bass note from the open strings around it at various points.
She is pretty good I have to say, she's been doing this since she was 3 really...I just found that back then, when all she did was bash the strings, it was less annoying if the guitar was tuned to a chord!!
When she gets older I'll start to show her standard and Dadgad tunings, another game I play with her is singing scales.... I think she'll have a head start and she enjoys it!
Lord knows she sings better than her daddy!!