I would go with Silver Lake try for a 2-bedroom.
or cypress pointe again try for a 1 or 2-bedroom.
both will show up on
www.skyauction.com
this take patience.
don't get efficiencies or anything with a min-kitchen. these rooms are smaller and he will probably need his space.
cypress pointe also is listed here
www.hotelkingdom.com
silver lake backdoor is about 1/4 miles from Disney. It is surrounded by disney in fact.
cypress pointe is close to DD.
you will need a car at both.
if you don't drive or don't want to drive. then stay on-site at disney. the value resorts are fine!!!
or rent points from a DVC member and stay at OKW - it is cheaper point-wise so money wise. in the low season (sept, oct most of nov and dec, jan) you can get a studio (efficiency) for $80, 1-bedroom for $160, 2-bedroom for $220. ($10 per point)
a studio at OKW has 2 queen beds plus a balcony - so you can still be in the room but outside while your child needs to nap. DVC resorts are WDW resorts so all the benefits of staying onsite.
that say - you can get a 2-bedroom timeshare using skyauction for $211.00 if you are lucky.