That's a different version than I know.

The goldfish is a quiet pet
He does not make a sound
He just swims round and round and round
And round and round and round
And round and round and round and round
And round and round and round
And round and round and round and round
And round and round and round.

He does not neigh or moo or cluck
He does not make a sound
He just swims ...

And when it is his time to eat
I know where he'll be found
He just swims ...

And when it comes his time to mate
I bet you fifteen pound
He'll just swim ...

And when at last he tried to speak
He tried to make a sound
The water ran right down his throat
And the poor bugger drowned
And drowned and drowned and ...

The tune I know this to is an old hymn - sorry, but I don't know the name of it.

Jacob