1. Log in to a Gnome session on Wayland.
2. Start Qt's online installer from the command line:

   qtrob@rob-desktop:~/Downloads$ ./qt-unified-linux-x64-4.3.0-online.run 
   

   On the command line you can read:

   Warning: Ignoring XDG_SESSION_TYPE=wayland on Gnome. Use QT_QPA_PLATFORM=wayland to run on Wayland anyway.
   

3. Cancel the installer.
4. Do as the installer told you:

   qtrob@rob-desktop:~/Downloads$ QT_QPA_PLATFORM=wayland ./qt-unified-linux-x64-4.3.0-online.run
   

   The installer exits immediately:

   Warning: Ignoring XDG_SESSION_TYPE=wayland on Gnome. Use QT_QPA_PLATFORM=wayland to run on Wayland anyway.
   qt.qpa.plugin: Could not find the Qt platform plugin "wayland" in ""
   This application failed to start because no Qt platform plugin could be initialized. Reinstalling the application may fix this problem.
   
   Available platform plugins are: minimal, xcb.
   
   Aborted
   

Because of issues like LP1958684 it seems to be a good decision to not use Wayland. The instruction to use QT_QPA_PLATFORM is just not helpful when the installer was built without the Wayland plugin, so it should not be shown.