If you want to start a new window of your application in the same process, you can just create a new instance of the window class that Quickly created for you.
My app is called quickly-gtk, and in the python module ./quickly_gtk/init.py I have the following lines (at the bottom of the file):
# Run the application.
window = QuicklyGtkWindow.QuicklyGtkWindow()
If you call that again it start a new instance of your primary window. However, the code Quickly produces is really meant to run one instance of this window at a time, so you will have some side effects you will need to code around.
For example, Quickly connects the window closing event to a callback that ends your whole process. If you have multiple windows, you'll need to override the
on_destroy() method of your window. There are likely to be other issues you'll come up against doing this.