Ozark Jubilee was the first nationally syndicated country music show, running from 1953 to 1960 or 61. It was broadcast from Columbia, Missouri, and was hosted by Red Foley (whom you can see talking a bit strangely at the end of the clip). The song is L'il Liza Jane, played by Bill Wimberly's house band, with Thumbs Carlille and Curly Chalker.
There are quite a few clips on YouTube of the old Ozark Jubilee show. Click here for more.