Charlie moved from hammock to cot at 10 months, and Olivia from hammock to cot at 11 months, and this is when I started them with a pillow. In both cases I gave them the pillow I had used all the while breastfeeding them, so I am sure it smelt "comforting" for them?

If you are concerned, maybe make the cot up with the pillow UNDER the bottom sheet: that way they have the pillow, but zero risk of it smothering them.......