The first time we took our then 2 yr old dd to WDW the only character she saw was Pochahantas and of course, she wasn't at all intimidating because she was just a pretty woman. I didn't bother with any other characters because i thought she'd be afraid of them (because she was afraid of some she's seen at kid's birthday parties prior to that visit).
Before our next visit I got 2 videos, Mickey's Beach Party at WDW and Wilderness Party. They feature the characters and lots of singing and dancing with kids, she loves these videos. So, they introduced her to the characters. If you can't visit WDW as often as we do this is a good alternative to help her feel more comfortable with the characters since they dance and sing with children.
The next time we went in June she was just about to turn 3. We went to Garden Grille (in EPCOT) for lunch which has Chip, Dale, Pluto & Farmer Mickey. She was a bit apprehensive at first but not too afraid. The first round they made they signed her autograph book and gave her a "high 5" (she likes that). When they came around again, she let everyone but Pluto sit with her (but not get "too" close). It was a quick weekend so when we came home I had video she watched over and over.
By our next visit in September (3 mths later), she visited Minnie Mouse at her house and Mickey & Minnie in AK. She didn't like Baloo or King Louie though. And, on our last visit in December she saw enough characters to almost fill up her autograph book, loved posing for pictures with them and LOVES watching the video of them. Her favorites are Minnie, Mickey and Chip and Dale & Cinderella. So, it is possible your dd may outgrow that character shyness. She can see many of these characters at Toontown at MK, not just at the character meals.