I am also using Archlinux for Qt 4 purposes, and the issue is this:
QT += webkit webkitwidgets
^^^^^^^^^^^^^
The Qt GUI was separated into QtGui and QtWidgets in Qt 5. That also included the restructuring of the QtWebKit module to reflect the changes.
Therefore, in Qt 4, there were no separate widget modules. That means, you should only write the following and that will work:
QT += webkit
Notice the webkitwidgets
line removed. If you really fancy this, and wish to use Qt 5 later while being compatible with Qt 4, you could write this condition check:
QT += webkit
greaterThan(QT_MAJOR_VERSION, 4):QT+=webkitwidgets