Jim,
Getting to
Mickey's Backyard Barbeque is not the easiest thing to do. It always involves a few transfers, but it is so worth it!
Here is a rough plan to get there by 5:45 pm;
4:05 pm - Get to bus depot at Animal Kingdom park to take a bus to the Contemporary resort
4:50 pm - Walk from the Contemporary Resort to the Magic Kingdom resort boat docks
5:00 pm - Take Boat from Magic Kingdom to Fort Wilderness
5:35 pm - Walk from Fort Wilderness Marina to Mickey's Backyard Barbeque
5:45 pm - Arrive at Mickey's Backyard Barbeque
Now a few notes.
There is a boat that goes directly from the Contemporary Resort to Fort Wilderness, but I think you are better off for frequency to walk over to the Magic Kingdom.
I have padded in 20 minutes of waiting time for each time you are grabbing a bus or a boat. That is because you could find yourself waiting that long at any of these transfers. Odds are you won't wait 20 minutes at each, but better safe than sorry. And if you get there early, that gives you more time to explore the Fort Wilderness Resort area!
BOTTOM LINE: I am one who hates arriving late to a reservation. It is even worse for a dinner like this, where everyone is seated at the same time. Or in this case, let in at the same time. I would urge you to be at the Animal Kingdom bus depot no later than 3:30 pm, to be safe. You are there during a busy summer time, when more delays can occur due to crowd levels.
Have a magical (and delicious) vacation!