My youngest was 23 months the first time we went. I did wind up holding him quite a bit, but he was bigger than my 4yo. We owned a backpack style carrier, but that was way to big to carry around the parks and it would have been a pain to keep getting him in/out.
We have since gone every year (either May, Sept, or Aug) and we have mostly been able to avoid waiting.
Get to the parks at rope drop (especially AM EMH) and use FP to do all the major attractions with minimal waits. During busy park hours we mainly do the less popular attractions, shows, just walk around and soak in the atmosphere, or enjoy our resort
I remember that first trip I did all this obsessive research and was convinced from posts here that I had to bring things to keep the kids occupied, but after the first day I left all that stuff at the resort. My kids were perfectly content to look around at the scenery in the queues, talk about what we had already done and what they wanted to do next, and maybe have a snack.