We took our youngest DD to Disney World at 3 months and Disneyland at 11 months. It had been many, many years since we had visited WDW and our first time at DL.
We took her on some of the no height requirement rides at WDW.
Just keep in mind that there is a dark drop in Pirates (2 drops at DL).
I went on Peter Pan's flight and the ship leans forward a little bit at times.
I read that you cannot ride with the baby in a baby carrier and so we did not even attempt that.
At DL, some of the older rides are jerky even if they don't have a height requirement (snow white's and mr. Toad's).
The canal boats were relaxing but still made me a bit nervous when getting in and out
Casey Jr's train and Jungle Cruise are other things we rode. And of course it's a small world. Haunted mansion was fine also.
In DCA, there are Ariel's ride and several rides in Bug's Land from what I can remember.