We don't have children, but WDW has always been our "happy place." We absolutely love it, and are happy to be heading there over the New Year holiday. We've been to WDW with family and children, and it's a whole different experience. When the two of you take the trip as a couple, you'll be surprised at how "free" your time is.
My sister (single, no kids) has made 2 trips to WDW by herself. The first one was just after 9/11. We couldn't get to the mainland to meet her, so she decided to go it alone. After that trip, she realized it was easy to be there on your own because she felt safe being a single at WDW, and went again earlier this year. She had no trouble finding people to chat with, etc.
I hope you have a terrific time. When you're there, take a look around. I think you'll be surprised at the number of childless couples you'll see.
Enjoy!!!