On Linux, compilers and IDE's are usually seperate projects. Your VL install probably already has a C compiler (gcc) and a C++ compiler (gcc-g++). I agree with kidd on kdevelop. Not that I tried any of the other ide's, but I really like kdevelop, and it's easy to install. You should be able to install kdevelop with gslapt or
slapt-get --install kdevelop
As for Qtdesigner, it's probably already installed (it comes with the qt package). To start qtdesigner for qt3 use "designer", to start qtdesigner for qt4 use "designer4".