Great work has been done by the Mozilla and Nokia mobile browser teams. As result we have a working Qt port based on the latest Mozilla trunk 1.9.x.
The port is fully compatible with the official Qt 4.4 release. It is also ready to run Firefox3.x and the TestQEmbed reference UI:
You can download and try this X86 build
Sources are available for checkout and building from: hg:mozilla-qt branch.
Build instructions available in the Mozilla Wiki.
This port is not official yet, but we are working on it, see: bug 448989.
Additional information is available on Vlad's blog.
Feel free to build and test; if you have problems, please report them in Bugzilla.
Patches are welcome.