Write a web app, likely in Django - the docs will teach you a lot of good Python style.
Use some of the popular libraries like Pygments or the Universal Feed Parser. Both of these make extremely useful functions, which are hard to get right, available in a well-documented API.
In general, I'd stay away from libs that aren't well documented -
you'll bang your head on the wall trying to reverse-engineer them -
and libraries that are wrappers around C libraries, if you don't have
any C experience. I worked on wxPython code when I was still learning
Python, which was my first language, and at the time it was little
more than a wrapper around wxWidgets. That code was easily the ugliest
I've ever written.
I didn't get that much out of Dive Into Python, except for the dynamic import chapter - that's not really well-documented elsewhere.