All the parks have baby centers with rocking chairs, highchairs, changing tables etc. I believe in all of these centers there is food, diapers, wipes for sale. And usually all shops have diapers just ask, they're behind the counter. If your looking for souvineers....I'd bet just about anywhere. We have gotten "Baby's First Christmas" stocking at the Christmas store at DTD. Last year, my DSIL brought back a pink onesie style shirt with Minnie's on it saying WDW.
Hope that is helpful.