<p>I know it's possible to place a PyCairo surface inside a Gtk Drawing Area. But I think Qt is a lot better to work with, so I've been wondering if there's anyway to place a PyCairo surface inside some Qt component?</p>

Qt's own OpenGL based surfaces (using QPainter) are known to be much faster than Cairo. Might you explain why you want specifically Cairo in Qt?
For the basics of using QPainter see
this excerpt
from the book "C++ GUI Programming with Qt4", and while it's C++ code, the PyQt implementation will be parallel.
As for joining Cairo with Qt...
This article in ArsTechnica
sheds some light - it seems nothing that could help you exists currently (iow., nobody tried such marriage).