Suggestions to take care of the pillow cover:

When the pillow case is washed, the picture drawn will wash off but the white might not be so white anymore, maybe some hues of the color remain...It will not distract from creating the next drawing. There are some products on the market that will absorb the color. (Woolite - Color Protection and Shout - Color Catcher) 

Best to draw on a flat surface and not on the pillow.

I also suggest that your child sleeps on the Butterfly print rather than what they have drawn to avoid direct contact with the colors even though they are non toxic and water based. Be sure the colours have dried before putting the case on the pillow and you might want to put another pillowcase under this one.

Better not to sleep on the pillow with wet hair as it might smudge the drawing and upset the child. Enjoy, dream and manifest good...