The launcher for your program in fact is a
.desktop file, currently living in your Desktop folder. Move (or copy, if you also want to leave it on the desktop) that file to the hidden folder
.local/share/applications. It will then automatically be included into the Applications. From the Applications overview, you will be able to pin it into the dash (run the application, then right-click on the icon in the launcher and select "Add to favorites").
.local is a hidden folder in your home folder. Turn on "Show hidden files" in the file manager (tip: you can press Ctrl + h to quickly toggle the setting).