I was learning on my sister's baritone uke at that age. Some of the songs we did were ones we still sing: Desert Silvery Blue, Grandfather's Clock, The Seine, Polly Wolly Doodle, Hush-a-bye, Froggy went a courtin'. There are more listed in this old thread. That thread also has a link to Kadittles (sp) which is ALL kids' songs.

Have fun!