I upgrade KDE fairly frequently. My last KDE upgrade was from KDE 3.1 to 3.1.3 on August 10.
KDE is very finicky about dependencies. You usually cannot mix KDE packages from different releases, i.e. a mixture of 3.0 and 3.0.3 will not work. This release strictness also extends to the Qt version underlying KDE.
I am happy to report that 3.1 to 3.1.3 was the easiest I have ever done. It seems that a mixture of 3.1 and 3.1.3 will work, which is exceptional for KDE.
Even so, before you start the install make sure that you have all of the KDE 3.1.3 dependencies including Qt, xmllib, xsltlib, and the art package. If you get part way through the upgrade and find that a dependant package is missing then you can probably download the missing package and install it even with a mixed KDE, but with KDE I would never push my luck on missing dependencies.