Hi, I just had to reply to your problem seeing as we had exactly the same issue on our trip last year when my daughter was a similar age. She was extremely afraid of any Big Head characters at home -- I really thought this might ruin our trip. It turned out OK. Here's what we did (most already mentioned by other posters but I wanted to assure you that this worked for someone!

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1. We watched the Disneyland Fun video as well as the other sing-a-long songs ones that feature the live action characters with kids in the parks. Beach Party and Campout are the others and she still loves them. We talked about how WDW was going to be a lot like this in real life.
2. We spilled the beans on them being people in costumes. Kinda left it ambiguous -- like Santa, Mickey, etc can't be everywhere at once. The characters need helpers to be able to play with all the children all over Disneyworld. We told her that the princesses (and anyone whose face you can see,) however, are the real thing! We let her know that this is a "grown up secret" and she shouldn't tell the other kids around who might be disappointed. She was OK with this.
3. We let her know that in the end, if she still didn't want to go near them, it was fine. We told her the characters understand if some kids are shy around them. We even went so far as to send her an "invitation" to WDW from Mickey and Minnie where they assured her that if she wanted they would only wave at her from far away.
4. On the trip, we took our cues from her, and surprisingly, from the characters themselves. These people are so good at easing a child's apprehentions, they were so gentile and never pushed it. They got reactions out of her I never in a million years would have dreamed possible. By the end of the trip -- and I get misty thinking about it -- she was actually enthusiastically hugging her favorites. On our second day, her favorite princess, Mulan, took the time to actually cross the street, get down to her level and have a 5 minute conversation with her. Another time, we saw Piglet and let him know that she was shy around the characters and he interacted so nicely with her and even signed her book "to brave Katie." Especially if you let the characters know up front that your child is uncomfortable they will treat them accordingly and let me tell you from experience it worked wonders.
Sorry this was so long! Hope you have an amazing trip!