1) Do bring a stroller for your child as there is much walking and your child need to take a nap in the afternoon. JR is the most convenience means of transportation and most of the stations have elevator/esclators for strollers, it is not difficult to use a stroller.
2) No need to buy ticket for child under 4 yr old. For buffet (e.g breakfast) at hotels, they don't charge infants and you can take some of the porridge/rice out as baby's lunch.
Tokyo is good for travelling with baby/small child. Don't aim for going to a lot of places during the short stay. Just relax.