How did u manage to pass the deliver baby???

In my experience, it's completely random. I've played through the Doctor profession with 3 different sims, and it was different each time. My first play, it took around a sim week and a half before a laboring mom-to-be showed up. The second only took two sim days. The third was just shy of a month in sim time. If memory serves me correctly, the "deliver baby" task stayed active for as long as the wait took and carried over day to day. It's been a while since I last played a doctor though, so I can't say it's true with certainty.

You can try to wait it out and see, or use a cheat to get past it. It's really a matter of how much time you are willing to sink into it.