Mo, one reason why I like "Little Bunny Foo Foo" is its ending line.
I'm sure you probably 'got' that that line is a witty play on words of the saying "here today, gone tomorrow".

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http://www.answers.com/topic/goon gives these definition for "goon"

n. Slang.
1. A thug hired to intimidate or harm opponents.
2. A stupid or oafish person.

{3}[Probably ultimately short for GOONEY, simpleton.]
-snip-

I think that the #2 and #3 meanings are most applicable to the meaning of goon as it is used in that song. However, it was because "Little Bunny Foo Foo" was 'bobbin field mice on the head" and didn't heed the warning to stop doing so, that he {or she} was turned into a goon. So I guess there's an element of the first definition in that song too.

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YouTube has 455 video hits for the title "Little Bunny Foo Foo".
Here an example of this song that I thought were kinda cute-ignoring the fact that kids might like the boppin on the head action & references in that song:

http://www.youtube.com/watch?v=aoFzaUo3PZ4

"Little Bunny Foo Foo" is also featured in this videotaped medley of children singing songs:

http://www.youtube.com/watch?v=8aVy7TDTaFk