Congratulations!! I know when my mom found out we were having our little one she had a trip planned soon thereafter and it was surprisingly a little tough for her to find items for infants (toddlers, a little easier) I believe she found a cute Minnie outfit in the Briar Patch/Winnie the Pooh store near Splash Mountain in the MK and a few things at the marketplace.
As before mentioned there is a room in World of Disney at the marketplace (disney springs) that had a pretty decent amount of infant layettes, suitable stuffed animals and some toys. MouseGear (the huge store at Epcot) also had a bigger selection of infant items (bibs, clothing, etc..). We took our 14 month on a more recent trip and came home with Disney duplo blocks from the
lego store for her, a set of big chunky plastic figurines (they kind of look like bath toys) that included Mickey, Minnie and the Gang, and a similar set of Star Wars toys (These said 2+ but were in a lot of stores and didn't have any small parts). There's always plenty of plushys/stuffed animals too in a lot of the stores--just look for ones without plastic eyes and get the sewn eyes instead if you are looking for an infant.
You could also check out the Art of Disney at Epcot (near Spaceship earth) or at the Marketplace or the Animation Gallery in the Studios for some seriously gorgeous art to make a Disney themed nursery (pricey, but unique, and often something you won't find elsewhere outside of WDW)
If you want to find Disney stuff at home we found a lot of the local JC Penney's have a pretty nice Disney section (though a little more for kids and toddlers) and the
Disney Store annual sale is going online right now (and in stores starting on the 5th!) Babies R Us stores have a decent selection too.