QtWebKit is not supported on Android as per this blog post:
Qt on Android Episode 1
As you can see in the "New Features" for 5.3, the original plan posted by BogDan has not changed in that regard:
Qt WebKit:
* Support for HTML5 Video Track. Subtitles and captions for HTML5 video.
* Support for Indexed DB API. See http://www.w3.org/TR/IndexedDB/
* Improved support for Mac HiDPI mode
I think your best bet is QtWebEngine
for 5.4 the earliest. Digia and the Qt Community as a whole switched to that a while ago, which was "announced" during the Qt Contributors Summit last year in Barcelona by Lars. In my understanding, QtWebKit is more or less in maintenance mode, but at least not as heavy feature development as it used to be.