Hi Abby,
Thank you for stopping by the Disney Parks Moms Panel with your great question. What a magical gesture you are planning for your friend's child, I can only imagine how excited they will be when you present them with the surprise!
Character appearances can be very fun as the characters are larger than life and love to let their personalities shine through. Characters will typically sign most items and pose for pictures if they are deemed appropriate. It is always up to the character's discretion, and they have every right to say no, if they aren't comfortable with the request. In the past we have asked some of the Princesses to make a short video saying hi to our friends back home, and sent get well soon wishes as well. What I would suggest is to ask the character's handler (the Cast Member that is standing with the character, who is usually wearing blue and white) if it would be okay to take a picture of the character holding the stuffed animal. The Cast Member will usually give you the okay, but then, I like to ask the character as well, to be polite. I have never had a character or Cast Member deny my requests, but it never hurts to ask first.
Another suggestion would be to have one or possibly two pictures taken with the characters and stuffed animal and then have the rest of the characters sign a photo mat to frame the photo. You could also have the characters sign a pillow case or a storybook as well.
I hope you have a magical time at Walt Disney World Resort, Abby. Please let us know if you have any other questions, we are always happy to help.
Stephanie