Are dolls even permissible in Islam? Images of people are not.
Yes. Under Sharia you can play with a doll up until puberty. As far as I can tell puberty is subjective under Sharia.
Aisha the 9 year old wife of Muhammad whom was 53 years old was playing with her doll when Muhammad came into the room and asked to put the doll away. The mother was asked to leave her daughters room.
She wasn't allowed to play with the doll again.