Epsilon Rose's answer covers the official rules perfectly. I've been both a PC and GM in games that involve pregnancy and childbirth, so I wanted to offer some ideas for things to think about in your game.
In General
Any of the suggestions below can be handled through role playing or using 5Es mechanics. Feel free to ignore any of them that don't fit into your game.
If the GM decides to play this in detail, I would recommend picking up one of those weekly baby update calendars/apps. They usually offer a lot of interesting tidbits that the GM and PC can both use.
Note also that this may make some players uncomfortable. If they are on board with that, it's okay. Many players will be unfamiliar with pregnancy either because of their age, lifestyle, or sex. It's also outside the scope of the typical adventure story, which eschews everything not related to the adventure.
While Pregnant
- Damage done to the mother may harm the child. In combat terms, even a small amount of damage could represent a mortal risk to the baby. This adds an unusual dynamic to combat.
- Restricted mobility. If you want to handle this in game terms, it may hamper out of combat movement, speed, and Dexterity rolls.
- NPCs may (and probably should) react to the PC differently. How exactly this happens will depend on culture of the game world.
- Gestation takes a long time. Changes are very slow. Conventional wisdom is that humans gestate for 9 months. Think about how long 9 months is in game time - all of Lost Mine of Phandelver can be played in the first trimester.
Birth
- Birth may deal non-lethal or lethal damage, both for the mother and baby. It is entirely feasible for the heroic PC to die in childbirth.
- Medical complications are myriad. In my experience it's best to hand-wave the details unless they are a part of some sub-plot or story arc - or if you are playing with a group of med students.
- For a midwife or other NPC, the Heal skill is what should be used to assist with birth.
- Birth is not a short-term event that is handled in a single scene. It may take a PC out of commission for several days.