Note that even if you build statically, there is no guarantee that another Linux system will have the same set of system libraries required to run the executable. A number of the libraries in the ldd dump above have nothing to do with Qt, and are not required in a functioning Linux system.

The typical way to distribute executables under Linux is to either package them with something like RPM, which builds dependencies into the package and allows the installer to download those if needed, or to simply tell the user what they are likely to need and let them acquire/install it themselves.