You need to ship the frameworks as part of your app bundle. You shouldn't depend on the user having to have home brew installed either.
For example, I use the following when linking:
QMAKE_LFLAGS = -Wl,-rpath,@executable_path/../Frameworks
QMAKE_LFLAGS = -Wl,-rpath,@executable_path/../Frameworks
To copy to clipboard, switch view to plain text mode
When you link your application with the above in your profile, it looks for the Qt frameworks relative to your app's executable in the app bundle at execution time. You can see what dependencies your app has by using the otool command, for example "otool -L /path/to/your/app/executable".
Also, it seems you might not be using macdeployqt. It copies the Qt frameworks into your app bundle, etc.
Good luck.
Bookmarks