You can fish just about anywhere in WDW. There are a few designated spots that you have to pay. I often bring a pole and fish around the canals and ponds at the resorts I stay at. One tip is you do not need a FL fishing license since Disney is private property.
Obviously, try to avoid boat traffic areas, landings, and other congested areas. Go early before most people get up. Fish bite better, too. Also, a guided trip may be a treat. The guides are great. And you will catch fish.
Florida waters have some yucky bottoms. Use spinnerbaits and buzzbaits (lures that stay off the bottom) for bass. I think you can rent poles and buy worms for panfish. I have seen anglers walking the shoreline around WL catching fish.
Good luck!
JB