A 24" needle for a toddler hat will require some sort of looping with the cable I'm sure. Does the pattern have instructions for how to deal with this? Can you link to your pattern?
Will your circ cable allow you to pull a loop of it between stitches so you can knit a smaller diameter on it? It depends in part on the length of the cable and in part on how flexible the cable is. There are videos in the Free Videos section for Magic Loop knitting.
HTH and just doesn't add to your confusion.
ETA When using a loop or 2 loops on a circ to allow for smaller diameter knitting, generally speaking more cable is better than less cable.
Happiness is catching that dropped stitch while it's still fixable..