I'd recommend skimming through a few Django applications to get an idea of structure, one I know off the top of my head (as I wrote it): https://github.com/zapier/django-knowledge
Read the excellent Yipit Django blog (http://tech.yipit.com/). Especially their post about learning Django: http://tech.yipit.com/2012/02/28/183772464/
I don't agree that the documentation is great, but it is definitely good, although it is frustratingly lacking in some areas - although you won't run into that soon.
My suggestion is to try it in this order:
1. Django Book
2. Django Project Intro[1]
3. Django by Example[2]
The best tip to learning Django is to use #django on freenode[3]. People there will not do your work for you, but interactive live help is simply the best there is, unless you know forums like Something Awful where you can write out long-form questions to people who'll respond in the same fashion.
EDIT: I seriously wouldn't bother with any of the Django (book) books out there.
[1]: https://docs.djangoproject.com/en/dev/intro/
Introduction to Django http://pyvideo.org/video/604/introduction-to-django
and if you want to venture further down the rabbit hole
Django in Depth http://pyvideo.org/video/610/django-in-depth
If you have any MVC framework experience at all django is relatively straightforward.
In short, if your Python skills are passable, I'd say the docs at djangoproject.com[1] are more than sufficient. If not, I'd guess you might have troubles.
I should probably also point out that I'd only dealt with web languages before that point (PHP, ASP Classic, etc), so that's probably a negative point for me.
Everybody's different, for sure. For me, my Django suffered until I understood Python.
Can I ask what your pre-Django experience was? I wonder if there's any significance.
To be honest, I suspect my Python's not great - I probably ought to spend more time just writing Python - I'd hazard a guess that less than 20% of the time I spend building websites with Django is spent writing Python (most is probably spent fiddling around with HTML/JS). I can always get by - but every once in a while I learn something new that I wish I'd known about long before (I remember learning about list comprehensions at an intro to Python talk at Stack Overflow DevDays after I'd been using Python for about a year!).