Our daughter slept pretty much through the night at 6 weeks.
Once we got her on the schedule, we could tweak it a little each time her sleep patterns changed..
She did become very ill at one point and we allowed her to sleep with us, it took forever to get her out of our bed.. so be careful about trying it, if you are really not into it.
Here is how we got her to sleep in her crib starting at 6 weeks.
You need to make sure you have a night time routine.
In the evenings make sure to have a nice quiet dinner, no TV no Cell phone calls, keep the areas your child is in as calm as possible. Then a nice warm quiet bath with nice strong massage like bath strokes. The more you get her riled up, double that time to calm her down. She is more aware of all of the interesting stuff going on and does not want to miss out. If you make it seem boring, she will stay more calm.Have her room ready when you walk her in there.
Feed her while listening to quiet music or a book on CD.
How is her room set up? Does she have a fan, quiet music, night light? Does she have a lovey? Is her room dark enough?
When you get up to feed her at night, do it with the lights off, only work by the light from the night light.
Do not speak with her or engage her. Keep your face blank. Change her in the dark and feed her in the dark. Lay her down and walk out. Again she may cry, but just check on her, without comment.
Feed her and then lay her down and pat her on her back..
If your child is still an infant, place her head up against the corner of the crib. That pressure will mimic the pressure that was in your womb.