my son rolls over in his sleep sometimes, hes 4 1/2 months old. it freaks me out when i look over and hes on his stomach with his head down, and i kept rolling him back over lol but everyone kept telling me he'll be fine if i leave him and i shouldnt worry so much about it. now when he rolls over he lifts his head up, even when hes asleep. he doesnt have a pillow or anything yet still.
im sure it'll be fine to put a pillow in the crib, i keep being told babies know when they need to roll over and if they cant breathe (well after a certain age, and im sure at 11 months your daughter would be able to)
maybe try it and just keep an eye on her for the first few days? like before you go to bed just check on her every now and then and eventually you'll start to feel better about it.