On our honeymoon, my wife and I scoffed at the parents who brought kids that seemed to be too young to comprehend where they where, much less get enjoyment out of it. By our second trip, we were scheming ways we could make that situation work for us.
Well, this past trip was our first attempt at seeing how this would play out. It was good is some ways, hard in others.
My first piece of advice is to take it slow. It was not possible for us to keep the same pace we used to (much to my frustration at some points).
Also, take full advantage of the Baby Care Centers. There's one in each park and, while I don't know where they are in the other parks, in Epcot, it's located conveniently in the middle of the park, right between Future World and World Showcase on the Mexico side. My wife will have a more detailed review of the Baby Care Center soon, but I will leave you with this: it was probably the best tool we had in our arsenal that day.
One of the things we did was buy her an autograph book that had a place for pictures. We would get a character to sign one page and then we will print off a photo of us with said character and put it on the page next to the signature. It will be a fun memento to put in her baby box. Of course, she was more interested in the pen than seeing the characters, but she did really well. The only time she freaked out was when she thought my wife was about to hand her over to Daisy (really, my wife was just leaning in for the picture).
On the rides: We were lucky enough to have my parents down there with us and my mom isn't a big fan of the rides anymore, she just loves being at Disney with her family. She watched our daughter while we rode the rides. If you're not as lucky as we were, you can always use the baby swap system. You both stand in line, when you get to the front, one of you rides while the other stays with the kid, when your spouse returns, you swap.
The other part we thought would be an issue was the fireworks. At the end of a long day, the baby was tired and fussy and we had already decided that we would leave the fireworks early if she couldn't handle it. Turns out, she loved them. Her giggling and laughing brought the attention to everyone around us.
One thing I wouldn't suggest is park hopping. Stick to one park for the whole day. If you leave, go back to your room, not another park. That was probably the hardest part of the day for us.
Over all, the day was a lot of fun - but we definitely learned how to do things a little differently next time.