It doesn't seem possible that anything more could be said about this simple song, but I'm going to add that I learned this song in school, and we sang:

   I had a rooster and the rooster pleased me.
   I cherished my rooster 'neath the green bay tree.
   My little rooster sang cock-a-doo-doo etc

The animals' cries built up, as usual, but the final line was a cock-a-doodle-doo that went up high and came down low to end each verse with a flourish.

I never cared for the song, but it has stuck in my brain for 55 years.