Actually, WDW is the first place we ever left our kids without a babysitter, I think when they were 11 (girl) and 9 (boy). We felt comfortable leaving them in the room together - staying at Boardwalk and going to eat at Flying Fish, for example. It's right downstairs! They had a phone, we had a phone, and we'd call them a couple of times. At home, we waited a couple of more years before leaving them home alone. And alone meant with each other - if we had plans, they had to be home together.
We used to take them with us to restaurants like FF and Yachtsman, but they were miserable, and when the kids aren't happy, neither are we. They are teenagers and still don't like long dinners out...I'm looking forward to leaving them in the room in exactly 3 weeks to go eat at BlueZoo!