while trying to setup a new system I wanted to copy some menu settings I had. Alacarte is a great tool, but as with most gui tools get tedious when you have multiple similar actions. So after digging around I found the two directories of interest: ~/.config/menus and ~/.local/share/applications.
The menus directory has an XML file called applications.menu which contains the structure and points to *.desktop launchers in the ~/.local/share/applications directory.
copying the desired files from these directories should re-create your menus on the new system.