Some rules of thumb:
distance between eyes and mouth – closer together for children
Shape of face – rounder for children
Bridge of nose – less emphasis in children
neck – thicker in children
head – larger
You have the round face and large eyes already. You can try smoothing out the bridge of the nose to emphasize it less, thicken up the neck a bit, move the eyes down a bit to decrease the distance to the mouth. Cartoon kids also have less distinct jawlines (goes along with the thicker neck) so try for a smooth transition between cheek and neck rather than a pronounced jaw when seen from the side.
Here is a photo of a young girl: notice the compression of her features, lack of jawline and puffy cheeks, nose bridge almost non-existant, wide neck, round face…
Follow real life proportions for cartoons. Cartoon characters aren’t distorted, they are stylized. What is the difference? For example: the nose will be in the same place on the face, but may be extremely long, or very short, or round. Eyes are placed in the center of the skull (proportions) but may bug out or be oversized or beady (stylization).
Hope that helps. Looks like you have a good start.