I agree that a one-bedroom villa would fit your needs well. They feature a living room with sofa bed (a pretty comfortable one), full kitchen, washer/dryer, separate bedroom with king-size bed and a dual-style bathroom with vanity and jacuzzi tub in one area and shower, toilet and another sink in an adjacent area.
I agree Animal Kingdom Lodge Villas would fit your needs. It is the closest property to AK, but considerably farther away from Magic Kingdom. Note also that AKLV is not close enough to AK to walk. You must take a bus or drive.
Another possibility is Wilderness Lodge Villas. They have boat transportation to the Magic Kingdom, which would be convenient with your toddler. Also, Saratoga Springs Resort and Old Key West resorts are close to DownTown Disney and have boat transportation to and from there. There is no resort that is close to both Animal Kingdom and DownTown Disney -- they are pretty much at opposite ends of the WDW property, which is huge.
Finally, if you and your DH want good restaurant options, you might also consider the villa properties near Epcot -- Boardwalk Villas and Beach Club Villas. There are more restaurants within easy walking distance in the Boardwalk/Beach Club area than anywhere else -- considerably more options than at DownTown Disney.
You can rent points from a Disney Vacation Club member for a stay in a one-bedroom villa. Or you can book directly with Disney reservations. We book directly because if you stay on a point rental, you don't get daily maid service or turn down service (just every few days), the point requirements skyrocket on the weekends, we don't like turning a couple of thousand dollars over to a stranger, and stays booked with WDW reservations are much easier to cancel than a stay on rented points.
Enjoy your planning!