Reinforce those live performances with recordings of the show or by the artist. Allow your child plenty of imaginative singing time alone with the recordings. Your child may dream and dance while singing. Mugging in a mirror is highly instructive to the aspiring performer. Singing is a communication art.
Pitch requires maturity and control over the voice.
Listening is the basis of all musical experiences. Sing simple tunes with your child. Nursery rhymes, camp songs and church hymns all have simple tunes. Children breathe well naturally. Children won't need this level of voice training until their teens.