pillows, duvets, quilts, etc can be used from 1 year if you want to. My dd had her pillow from 1 year as she had a cold and it helped to elevate her head and also gave me somewhere to put the hankie with karvol on it to help clear her nose!!
Am sure DS had one at 1. First was a tiny one, but defo had a proper one by 18 months at the latest. Felt exactly the same as you - that it can't be comfy to sleep without one!! I always thought that by 12 months, they have the strength and the reflexes to push anything off their faces if it gets covered, and therefore pillows weren't a problem. Could be wrong on that though - no medical training!