But there is a historic (non-jazz) recording that is interesting to study: you get the full works, plus the lyrics: Click here to listen. In this version, the Verse is in G; the Chorus in C.
The song changes to the related key (in effect, dominant to tonic) for the Chorus. This is the part on which musicians improvise. There are only sixteen bars and the Progression is straightforward (Think The Apple Tree Progression [I-IV-I] and The Four Leaf Clover Progression again).
Here is the tune. This is shown with the Chorus in Concert Bb - the key generally used in traditional jazz because it is the most comfortable for players.