Welcome to the world of J-dramas! :D
Yep, a usual J-drama have 10-13 episodes. I think this is because the series are shown by season (winter, spring, summer, fall). One season is three months. As the shows are shown weekly and there are four weeks in a month, 4x3=12. However, there are those which rarely get 16 episodes (e.g. Itazura na Kiss: Love in Tokyo), those which airs longer (e.g. Amachan), and, of course, the taiga dramas are exception as well because they're shown annually.
I hope you'll see and enjoy more Jdoramas! They tend to be more on point so the series don't get too draggy. :)