This balaclava pattern will help you to make a hat exactly like the pictured one! The pattern is for 0-6m, 6-12m, 12-24m, 2-4 years and 4 years to teen.
You will need DK yarn, knitting needles, a tapestry needle or crochet hook to weave in the yarn ends and also the same tapestry needle to graft stitches at the back of the hat.
Since the hat part of this is knit flat, you can use any knitting needles you like. I prefer using ether long circulars, or long straight “afghan” knitting needles. The neck part is knit in the round – so, you will need either double pointed needled or a circular needle to make a magic loop.

Regarding the yarn and needle size – you really have to make a gauge swatch to find the right needle size to match the gauge! Otherwise the sizing will be way off!

gauge: 17 sts in 4in/10cm in stockinette stitch