We traveled with DD when she was three months old. Had no problems. She didn't ride much, but that was because she spent a lot of time sleeping in the stroller. Took DS when he wasn nine months and he rode everything that didn't have a height restriction. Ok, maybe not the teacups and the astro-orbiters, but PotC, HM, Pooh, PP, etc.
The biggest thing we did was to try to keep DD cool. Spent a lot of time in shops or inside somewhere while part of the group rode. Then we'd switch off and she'd wait with someone else.
We're going back in June, and she'll be 13 months. This trip looks like it might be more difficult as she is very, very active now.