When did you start giving your child a pillow?

My son is 1. He has always been a terrible sleeper at night. And it's even worse now with 3 molars coming in at once. He seems to take better naps during the day if I lay him down with a pillow. But obviously that's during the day when I'm awake and can watch him and at night I'd be sleeping so I'm afraid of suffocation. I don't know if I'm being overprotective or not by not letting him have one at night. Was just wondering when people started to let their kids sleep with a pillow at night. I have friends/ family that say go ahead and give him one and I have some that say to wait til he is in a toddler bed. I just want some sleep.