I have used a litterbox for puppies and it has worked well. They make doggie litterboxes but you can just buy a big kitty one or some other tray of similar size to save money. And for the bedding I use wood pellets, get them from a farm store. They are made for bedding horse stalls, or you can get the pine pellets made for wood stoves. You can probably use some of the ones made for cats that are pelleted recycled paper too. Once the puppies are a bit older and aren't so paper shredding prone, I just line the litterbox with newspaper and it makes it easier than having stray pellets getting kicked around the house. They are not fun to step on barefoot! lol
Like Pat suggested, I would get an xpen, and a top for it, then set up a nice crate or bed in one corner and the litterbox in another. You can try the pee pads too, but I find mine liked to just shred them. Gating off the kitchen would best be left for a more trustworthy older pup/adult. Like others have said they are still good escape artists and kitchen cupboards are so tempting to gnaw on. You can do a lot to puppy proof the room, but there is still a lot of damage they can do that you probably don't want to see. lol Best to confine them in a more chew friendly area during those teething months.
Good luck with your new baby, I hope she comes from happy, healthy, well tested parents.