Hi Linda!
There are several great options at which to enjoy BBQ ribs at Walt Disney World.
As a Quick Service Meal,
Flame Tree BBQ at Disney's Animal Kingdom has a great, 1/2 Slab of Ribs which is accompanied by side dishes, soft drink and a dessert. It's a great option for lunch or dinner during a visit to Animal Kingdom.
For a Table Service meal, without visiting Mickey's Backyard BBQ, I have the perfect option for you and it's one of my family's #1 Favourites!
Whispering Canyon Cafe at Disney's Wilderness Lodge offers a fantastic, All You Care To Enjoy skillet, heaping full of Ribs, Pulled Pork, Roasted Chicken, Beef brisket and many delicious accompaniments and side dishes! It's a fantastic option and is indeed on the Disney Dining Plan. A children's option is also available including ribs and mashed potatoes with corn on the cob. Reservations are strongly recommended for this popular location and can be made online at the link above or by calling (407) WDW-DINE. To get to Wilderness Lodge, simply board a Disney Transportation bus from the parks or hop on board a boat from Magic Kingdom for a relaxing, short ride.
I hope you'll visit me again soon with more great questions! I could talk about Disney Dining all day long!
Wishing you a Magical time, enjoying ribs, at Walt Disney World Linda!
Kirsten