We changed from a grobag to a pillow & duvet (still in the cot) at 18 months, and then we transferred to a toddler bed at 2 years. At weekends we would bring Toby into bed withus for 10 minutes or so in the morning before we all got up and taught him how to pull the duvet up so he was 'snuggly' and he's been fine with a duvet ever since.
We got a cot pillow - a very flat one so there wasn't a great deal of difference from him sleeping flat in the cot, and now he's in a big boys bed he still has a very flat normal size pillow.
HTH
Sharon