The README has the pertinent details; in short, you evaluate the Envjs implementation (env.js), call a function to register the native Envjs/QtScript handlers (for network & file access, asynchronous function execution, and a few more things), and presto -- instant browser environment.
(jQuery 1.5.1 unfortunately fails with the error Result of expression 'ajaxLocParts' [null] is not an object.)
Well, Envjs version 1.2 is 680KB (unminified), so evaluating it isn't free. It's another tradeoff to consider. With V8, it would be possible to inject Envjs into the standard environment and serialize all of it, with the prospect of vastly reducing initialization time.
This project is open for merge requests. Not all of the native integration is implemented yet, and the XMLHttpRequest implementation could be improved. There's also the XML parsing issue (maybe an existing lightweight parser could be used instead of relying on E4X?).