In the last 1.5 years, we have stayed at AKL Jambo House, AKL Kidani, and Grand Floridian, and we requested and received a crib at each one. They are standard "hotel" cribs that we have also had at hotels on non-Disney trips (white metal rails, smaller than a full-size crib, but bigger than a pack-n-play - plenty big enough for my 2.5 year old DD on our last trip).
We requested the crib on our first stay at Jambo house because the pack-n-play in our room was visibly dirty, and they brought one no problem. They gave us a bit of a hard time at Kidani when we called to request one (there was no pnp in our room, though they seemed to think we were making that up), but they eventually brought it. At GF, the bellman who took us to our room just asked if we wanted a crib without us even mentioning it, and had one sent up for us with no issue. Definitely ask if you want one - they do have them, though they will likely direct you to the pnp first. Just be polite but firm in wanting an actual crib.