I am not an illustrator. I am a doodler and I doodle a lot in my notebook when I’m writing. If YOU are an illustrator you might find it helpful to see what Keri Smith says about how to start as an illustrator, OR what Cheryl Klein (of Arthur A. Levine Books) says you should have in your portfolio.
There are all kinds of illustration, and kid lit needs all kinds of illustrators. There are a lot of groovy illustrators that went to art school and do an amazing job. The pros always tell you that it’s crucial that you go to art school. I’m sure it helps, but if any formal training at all was required than two of the biggest names in kid lit illustration- Mark Teague and Mo Willems would be names you didn’t associate with dinosaurs and pigeons and the world would be a little grayer.