The pattern Amy uses in her sock demo "North Country Cotton Baby Socks" has sizes for babies and toddlers. I've made several pair from this pattern. You can vary the size just by using different weight yarn. I made two pair in fingering weight and three pair in worsted weight.
This is my favorite pattern for kids socks!! It's very basic, has good directions for a newbie, knit from the top down, and makes a great sock!!
You can also try Kitchner stitch to close the toe, which I REALLY love.
Happy sock knitting :XX: :XX: