My mom gave my brother a baby boy doll when he was really little (this would have been about 1981), and he loved it. He named him Scott right away. Immediately he stripped all the clothes off, and got a horrified expression on his face. He brought the doll to my mom and asked her "Mama! What happened to Scott's penis? Fix it!"
So my mother made little pink cloth genitals for Scott. And my brother was content. It's not weird that your son should want his erzatz baby to have all the same parts he percieves that he has.
It was a little sausage shape sewn to a little pillow shape, with just enough stuffing to make it fluff up, since baby genitals are little most of the time. Obvoiusly, there is no special sculpting necessary for soft-sculpture uncirced baby genitals.
For the nursing mommy doll, I've seen snap fasteners used for making the nipples (male side) and baby's mouth (female side). One example I saw had the snap edges carefully embroidered over with pink floss so it was not obviously a snap.
I'm not sure how I'd handle the belly, though! I design and make dolls, so I'd have lots of ideas. Velcro is good. Maybe an incomplete ring of loop on the body, open at the bottom just enough for the baby doll, with a seperate belly that hooks in place. Maybe, if you are doing female genitals, have the belly end partway down the vulva and that way baby comes out of the vulva... Or something.