I don't use Red Hat, so I'm going out on a limb here.
However, I believe the problem is due to Red Hat's packaging of KDE3. Both SuSE and Mandrake package KDE3 as separate RPMs which can coexist with your existing KDE2 packages.
Red Hat instead packages them as upgrades to KDE2 packages. So unless you force the installation, an upgrade of the packages removes the older versions. That would explain why you don't have QT libs 2.x.
If this is the case, then just download the Opera package that statically links the library (instead of dynamic). Or wait until Opera releases a package tested on Red Hat 7.3.