I guess a simple proxy server should have been an example in Qt Network module. What I mean of course a real proxy server based on Qt, not about using a proxy server via QNetworkProxy class. After all, there are other more complex examples like the torrent client and Google suggest (yeah, blame me for the latter). As a matter of fact, there are e.g. a gazillion proxy servers written in Python.
Look no more. I posted an example in the X2 repository, under the directory network/webproxy. The code is written for clarity and not for performance. In fact, fancy error handling is even omitted (minimalism rulez!). There is no support for pipelining, or in-memory cache, or per-connection thread, or even secure connection via https. I leave them as exercises for the curious readers.
If we focus on things which work, here they are: asynchronous socket handling, different request methods (GET/PUT/POST/HEAD), persistent connection aka keep alive, and even Flash and HTML 5 video streaming. Yes, you can still watch YouTube or Vimeo if you hook your browser into this little proxy. For a few hours of hacking and 92 lines of code (as reported by sloccount) and certain ways to abuse QObject, I could not be more happier.
There will be two other offspring examples based on this one. So stay tuned. Meanwhile let's just hope nobody would ask me for a colorful UML diagram for this snippet...
PS: Special thanks to Jan Erik for his feedback and review.