Oh yum. lol Kids are funny, aren't they? I am fairly certain this will be fine but I'd go ahead and call poison control. https://www.poison.org/ phone number is 1-800-222-1222. I've called them before myself and have had the nicest people just talk through things with me. They are very easy going and will advise you. Paper is often made of cellulose which is a harmless substance. It doesn't break down though so expect it to come out the other end. That's just my take on it but I'd absolutely call poison control to confirm or your child's pediatrician to ask them. I agree with your daughter though, ice cream sandwiches are good!
Children are careless and hence parents need to keep an eye on them all the time or else they may cause mishaps. I recommend you take your child to the pediatrician. They will guide you better as to what has to be done in such situation. I hope it is better now.