Depends but it also doesn't have to be that much more involved either.
Option 1: Multi-stage pregnancy that shows Jun's belly increasing in size as the days go by (I imagine pregnancy would last for days and not months because months would be silly). Let's say there are three stages before birth. This would involve keeping track of how long Jun's been pregnant, three new pieces of art for her per every currently existing piece (minus the intro), probably new dialogue mentioning the pregnancy as well as what stage she's in, and of course somewhere for the baby to go. Since an entire child-raising system is just... no... that's means the baby can either be a set piece in the apartment like the plushies you can buy to put on the couch, or you immediately put it up for adoption *ahem* Send it to daycare FOREVER.
Option 2: Basically the same as option one but instead of an involved, multi-stage pregnancy it's a switch that gets flipped. Either Jun is pregnant or she isn't. If she is, big belly, like, 6 months pregnant belly. If not, no big belly. Simple as. Whether or not she's pregnant and how long she's been pregnant would still have to be tracked, but this option would be easier on the art and writing.
Option 3: Pregnancy is now an end-state. You get Jun pregnant, fade to black. Cutscene. You managed to make millions working the stock market, and you and Jun move out of the shithole apartment into a house. Lady Annalie also moves in with you because she was always in love with both of you. Shanice visits every once in a while when she's not doing church stuff. And so the Courier who had cheated death in the cemetery outside Goodsprings cheated death once again, and the Mohave wasteland was forever changed.
*Fade in from black* So, you're finally awake.