The gauge is not given in the pattern. A different pattern in the book (Milly Mop) made with the same yarn on the same size needles has a tension of 28 sts and 36 rows to 10cm measured over stocking stitch using US 3 (3.25mm) needles.
Pattern also shows larger size hat (one size up to 10 years) using 1 x 50g Rowan D.D.K. or 1 x 100g Rowan Magpie.
With D.D.K., pattern suggests 1 pair 3.25 mm (no 10) (US 4) needles; 1 pair 4 mm (no 8) (US 6) needles.
With Magpie, pattern suggests 1 pair 4 mm (no 8) (US 6) needles; 1 pair 5 mm (no 6) (US 8) needles.