I'm not an expert but I am the proud 'owner' of a 12 week old DD.
Nine weeks (or indeed 12 weeks) is still very little and really they are too young for a real routine (in my opinion). So we just see it as trying to teach her good habits.
I bet, if you added up the sleeps, naps and catnaps that your LO has during 24 hours you'd be surprised at how many hours it adds up to. It seems that no matter what the pattern is, DD always has approx. 14 hours sleep in 24 hours.
Being awake for blocks of three or four hours is not ideal because there's nothing sadder or more frustrating than an overtired baby, when we know that all they need to do is relax and shut their eyes and it'll all be okay. In my experience the baby refusing to sleep and getting overtired is very normal.
If she's overtired during the day; a feed, a walk in the pram and a dummy will quite often tip her over the edge into sleep.
At night, we put her down (fed, clean and PJ'd) lie with her for a little while (we have a cosleeper cot) and she shouts every so often - I just talk gently to her and reassure her when she shouts (trying to distract her before she gets too angry), when she's more asleep than awake we retreat to the living room and just pop back to soothe and reassure her if she cries, and sooner or later the time between her crying gets longer and she falls properly asleep. Then we hope and pray we can get ourselves into bed without waking her.
We found a bath in he evening was too much for her, so we bath in the morning and just top and tail in the evening. And a dummy when she's overtired is a godsend - it seems to distract her from her fury.