How to write a python program that runs in docker container and keeps track of all the websites visited (url and visit start time)?

I want to write a small program that keeps watching all the websites I visit (url and visit start time) on my laptop. I'm also learning Docker and I want to make it in a Docker container that's running in background.

Can someone provide some clues/hints/directions as to how do-able is this application and how to write such a program? I'm in the python world, btw.