You need to either run Haiku gcc2hybrid or gcc4hybrid ( or Haiku gcc4 which will not allow running BeOS apps ).
Qt is compiled with gcc4. You are missing the gcc4 libraries required to run Qt applications. One of the above versions will fix that for you. Download & install.
The hybrid versions are the better choice of course but I listed all 3 possible options for you to choose.
Haiku’s official release is gcc2hybrid but if you want to run lots of gcc4 applications then I’d suggest going for gcc4hybrid instead - both will work but gcc4hybrid should have no or very few issues with gcc4 programs and still be very compatible with gcc2 programs.