Export all network traffic on a webpage
There is network monitor at Firefox dev tools. Take a look at mdn page where this feature is explained. It is possible to export HAR information from the Network panel by right-clicking and selecting "Save all as HAR". HAR is a network request archive format used by many performance and request analysis tools.
You can also use firebug addon which has also his own network monitor and extract data by using the netexport firebug extension.
For automated process (that will open the browser, then firebug, then the page and then will export data), you probably need the auto-tool used for testing firefox which is called mozmill