I guess the most plausible explanation would be that an immigrant worker women from asia had a unofficial affair with a local qatari (affair, rape ?), and she decided to go back home without the "problem", because it's not well accepted in her place to have a baby when you're not supposed to.
That could explain the quick catch of the father, one way or another.

The newborn baby was not easy to identify as oriental, asian or westerner (but not african, aborigen or papoo i guess), so they searched any women around that spot / timeframe.

Later on, catching / confirming the father.

Makes sense ?