We've gone with a toddler many times. We've never really let a toddler 'slow us down' so to speak. We still ride all the big rides, you just have to use rider swap. Often a child that age is happy to nap (partly) in a stroller.
Just to clarify, WDW uses height restrictions, NOT age restrictions. The list provided is good for a one year old, but older 'toddlers' can ride some of those.
You know the child best. It's best to be flexible.
Another thing to know/consider/ask about is that WDW is well designed with kids /families in mind. There are too many options to list here, but near just about every height restricted attraction is a kid friendly (mini) attraction. There are thing like interactive water fountains, little playgrounds, character greets, etc. Then again, at age one- characters might be a big scary! Probably your best bet is 'face' characters, like princesses -over characters like giant mice. your toddler may do best simply seeing the characters from a distance.
We like short split ups. Most the group goes on Space Mtn, one person takes the toddler on the Peoplemover or Buzz. Sometimes a toddler that age is just happy to people watch.
I agree with other posters, you don't have to worry too much about your child making a little noise here and there. That said, I'll go out on a limb- if the child is outright SCREAMING- it is may best to use a little prudence and take them to a quiet spot to cool off/tend to their needs for a few minutes. Your CM server will understand, and probably your fellow customers will appreciate your efforts.
Most of the time, if we see a meltdown, it's the parent who is having it. Probably the biggest pitfall to avoid is to simply keep your expectations in check. It's probably smart to avoid overplanning or over expecting. WDW stimulates your senses all day long: smell, sound, color, touch. (even taste) It can be tiring for anyone. We personally never plan more than one TS per day. I also limit the number of CC hold meals to like two per week. That way, most of our time is up to us. If we need a break, we take one. If we miss a ride- there's always NEXT TIME!