For Harriet (9 months) I used the smallest of the Worsted sizes and worked with this chunky yarn using size 4.5 and 5.5 mm needles (so the fabric is firm but not cardboard), you can adapt this idea to any of the standard yarn weights for the pattern.

I cast on in and worked the rib in the red.
I worked the first white row purl so as not to cause a purl ridge on the RS, except for the middle 3 sts which I kept in red and worked like fair isle, stranding the red yarn across each time.
I worked 1 section in white, working the 10th row as purl (avoiding the purl ridge on the RS again…do this for every section).
Next section I worked 6 rows in white, then I increased the centre red sts by 1 st each side on the next and following RS row (7 red sts).
Next section: change to red only, work 2 rows stst (so as to avoid having red and white sts in the same row - caused by the short rows) then work 3 more sections just in red.
(These instructions apply to the size I am working, you will need to alter them a bit for other sizes, maybe add a few more red sts for the nose stripe when working finer yarns etc)
Finish the hat per the pattern (I made 5 st cord ties instead of a strap).
Ears: I picked up 7 sts 2 rows in from the white section.
Work 4 rows garter st.
Next row: ssk, k to end.
Repeat for every row until 1 st remains, cut yarn and pull through.
I attached felt eyes and nose, you can use buttons depending on the child.

Thanks again to JoyBulger for the inspiration!
see Joy’s “The fox went out one chilly night”