Just like Rich's trick with QNetworkAccessManager, I have done something similar which I call tracenet (around 150 lines of code). Though I have committed this example to X2 some time ago, only now I have the chance to blog about it.
The idea is to subclass QNetworkAccessManager and reimplement its createRequest method so that we can keep track all the network responses and replies. This is useful for your network-based application, or even for e.g. QtWebKit. As a matter of fact, the tracenet example captures the network traffic as you load a URL into a web page.
Now, the next step is how to visualize the result. While it's certainly possible to craft a Qt-based fancy GUI for this (maybe using Qt Quick?), let's think outside the box. Unless you live in a cave, I am sure you are aware that there is this nice tool called Speed Tracer, part of GWT, an extension for Google Chrome or Chromium. For this purpose, we won't use the live profiling feature of Speed Tracer, but rather its ability to visualize network requests and replies (with nice timeline and so on). All we have to do is to carefully spit some JSON-formatted data that match the Speed Tracer data dump format. And that is exactly what tracenet does!
The screenshot below gives an exemplary result from running tracenet on my Nokia N900 when it accesses New York Times front website, a notoriously complicated web page. All I did was to execute "tracenet > nytimes.htm", transfer back the HTML file to the laptop and then open it with Chromium on OpenSUSE, click on "Network (resources)" line, and voila! You can click on each entry to get detailed timing info, use zoom in/out, and many other features of Speed Tracer. Refer to some tutorials if you are new to Speed Tracer.
If you want some follow-up and challenging exercise, try to split Speed Tracer code so that the pure GWT-part can run on any browser. Then you can just package it with QtWebKit and use it to show the outcome of all your network sniffing. Have fun!