As usual, I agree with OM. If you want your kids to enjoy their experience and nurture a lifelong passion in backpacking, making it enjoyable is paramount. Even with my kids today (10 & 7) I find meeting the requirement of being more than a mile from a road (common in many National Forests) to be challenging because trails are rarely straight or flat. Getting a mile away from a road usually means two miles of hiking and lots of hills.
My first trip with my eldest son (I think it is documented in the Hiking with Kids Section) was walking along a river bank until he decided we were done. Nice and flat and many interesting sights to enjoy along the way. He had a blast and I push him a bit farther now days
I also remember hiking with my son where we were wandering around looking at things (around 3-4 years old). He just kept going and going. I was really impressed with how far he was going, but the minute I said we should head back now, suddenly he was tired and his feet hurt and he needed to be carried. I said, "alright lets just explore a little bit more." Then we "explored" our way back home.