Start finding and collecting classical and contemporary monologues – toddlers and up to age 4 shouldn't have to worry about this.
For young children it can be short poems or cute children's short stories that they pretty much tell in their own words or even songs they like to sing. As they get a little older they can memorize age appropriate material.
If they sing, have different styles of songs ready with the sheet music in their key. There are several styles of music, but the most common styles for auditions are musical theatre, up-tempo, ballad, pop/rock and gospel.
Remember, you want to show off your child's personality, or the characterization of the role they are auditioning for, with what they sing. An example is you may know the National Anthem, but it's not a wise choice to use unless it is requested. That choice would show your vocal range, but it would not show very much personality.