Playful Kiss! :) They get married toward the end, but then there is another cluster of "after" episodes on Youtube that go through their married life. She gets preggers, and it's super cute. This is the Korean Drama version of Itazura No Kiss.
Queen of Reversals is exactly what you're looking for. It's an exploration of a marriage. They get married pretty early into it and have a child together.
This is a hard one, maybe wonderful days? They do get married and have a baby, but in the wrong order... And you also have Playfull kiss, but no children.
Good luck
Loving You A Thousand Times.. The lead couple married in the middle of the story and there is also a child involved. You can check it out. It's also a great drama.
You can try "tomorrow with you". They don't have kids in the drama but they get married by the fourth episode. It isn't one of my favorites but it's a good one. ^^