Hello, Katie!
First, thank you so much for reaching out to me. This is a GREAT question and one that was on my mind for awhile, so here goes...
Buzz Lightyear cannot actually sign his name, so he will use a stamp as his signature. This had me wondering how your little one's Buzz Lightyear doll would be able to really "take" his signature? Now personally, I have never seen Buzz Lightyear, or any other character, sign a child's doll, shirt, etc., it may/may not happen, but I do have two suggestions for you. First, prior to your visit, I would recommend having your DD take a picture of herself holding her Buzz doll. Then have the "real" Buzz Lightyear sign/stamp the actual photograph. Now this would be classic and you would be able to frame it and keep it for many years. This would be very personal for your daughter since she is in the photo holding Buzz and having his signature on the photo. Second, you can try taking your Buzz doll, but the Cast Members may or may not allow this. Again, I have never personally seen this done, but you never know. I don't know how the ink will hold up on the doll. I think having a picture with you will not only save you just in case you are told "no", but it will last for a lifetime.
Katie, I hope I was able to offer some suggestions that could work. I am so EXCITED that your little one will meet her hero, Buzz Lightyear! I would love to hear how this "magical" meeting goes! I wish you and your family the most memorable vacation ever. Please come back and visit me again with any new questions or needed advice. Have a magical day and "SEE YOU REAL SOON"!