(I am talking about default Qt's installation with shared libraries) basically You need QtGui4.dll and QtCore4.dll,libgcc_s_dw2-1.dll,mingwm10.dll these are necessity I guess and must be included along with binary.exe
From my experience they must be inserted into system32 directory. Other files you have to add along with binary.exe depends on the project specification.
You can set up testing environment in virtual machine with clean OS and install your application, check what's missing and successfully include missing dependencies.
Postresql as far as I know is not default db driver, so You need to add appropriate dll(s) as well.
Hope that helps
additionally this article is very helpful [WIKI]Deploying Qt Applications[/WIKI]
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