There was an ugly duckling
Who became a lovely swan.
—Oh! The goings-on.
The entirety turns on the "—Oh!" with the dash *preceding* the line. That is a clue for how to read the verse. This is no arcane rule; the leading dash derives its meaning within the context of the Silly Songs' punctuation scheme… it is the only time a dash precedes a line, signaling something special.
That is the kind of close reading good poetry (stay calm: we do not presume the Silly Songs qualify) rewards.
So, how do you read The Ugly Duckling? There is speed going into "—Oh!" but a significant pause follows. "The goings-on" is to be read as befits the particular character of the phrase. Who uses the phrase, anyway? We do of course but we already know how to read The Ugly Duckling. The intonation of "the goings-on" is a combination of exasperation, affection, superiority, wonderment— the tone that might accompany an amused shaking of the head, as in Good grief, what next?
We are happily to recite/perform Silly Songs. If asked nicely. Fees are reasonable.
*merrily, merrily, merrily, merrily, life is but a dream.
‡‡‡ Relative to How To Read a Poem, take a look at Ashley Bryant reading Eloise Greenfield's Way Down in the Music. It inspired the peculiar working of The Ugly Duckling. ‡‡‡