Very Hungry Caterpillar - Adorable baby gift or costume! This doesn't link to a pattern but is easy to accomplish by changing up the colors on an existing pattern, then adding the simple details to the hat. Would work for knit or crochet.
Adeline Fingerless Mitts or Arm Warmers, Easy Crochet Pattern with Faux Cables ( Free Pattern)
"Gorgeous crochet baby bootie shoe pattern with matching hat. Easy Crochet baby hat pattern suitable for a beginner, but also an easy crochet pattern to make cute baby shoes for a little girl. These are perfect for newborn"