Since you are running 12.2 which came natively with QT 3.x, you have a few choices in which will allow you to maintain a working system.
Correctly follow the instruction from the SlackBuild which was written for QT 4 and Slackware 12.2 ( http://slackbuilds.org/repository/12.2/libraries/qt4/
Correctly follow the instructions, and upgrade to KDE 4 and QT 4 from testing, you'll have to write info at slackware.com and express interest in obtaining this disc. Or perhaps some knows of a mirror that keeps previous testing/ directories populated.
Looks like T3slider got in before I did