We took our son at 6 months old and he went on everything that there was no height restriction for. Obviously, you can't take her on "thrill rides" like roller coasters, Splash Mountain, etc. and you can use the Baby Swap for that.
There really wasn't much that phased our son at that age. I had reservations about taking him on Pirates of the Caribbean and the Haunted Mansion but we tried it anyway and he was fine with both of them.
We are taking him back this Spring at 2 years old and I think we won't be taking him on those rides. He may really be scared at this age although I would love for him to go on them if I knew he wouldn't freak out. We'll see!
Have fun!