We went on a 4 night for our honeymoon last Oct and we thought it was perfect! I assume that Oct is "off season" so naturally there are less kids there, but at no point did I think "my god, we are surrounded by muchkins!!!" We had late dinner seating, and we sat with all honeymooners and I remember seeing only 2 children at a table somewhat near us. You'll see kids at the shows and on shore excursions, but I never found it to be "kid intense". I loved it! They crack me up!! Stay away from the Goofy and Mickey pool, though....it is swarming with kids!
Ultimately, Disney and kids go hand in hand. You'll see them there, for sure. But as many have said here, Disney does a great job of pleasing everyone! We are going again next October for a 7 night Eastern because we loved the 4 night so much!!
You'll have a wonderful time!