One thing you have to understand about kids is that they love doing what mommy and daddy do. They love to immitate. They'll get excited about hunting just because you take them out, but what I do (with my nephews b/c my son is only 2!) is explain to them that we're not always going to see deer. But I teach them how to find trails and how to find scrapes and rubs. They are amazed by this! They get so excited looking through my binoculars at a deer 400 yds away! I've never harvested a deer w/them by my side (for various reasons) but they still love it.
I would say that squirrel hunting would also be a good entrance into a world of hunting. In my case, my nephews love being with thier uncle and I with them. I make sure that when I take them I'm not planning on staying much longer than 2 hours in the field... because longer than that, it does get boring for them.
...and on that day when my strength is failing, the end draws near and my times has come, still my soul will sing Your praise unending, ten thousand years and then forevermore!