dumb question: What does "Cackling Stump" mean?

[javalorum]

No: HPFGUIDX 174727

I couldn't figure out the exact meaning of "Babbitty Rabbitty and her 
Cackling Stump". I thought Babbitty Rabbitty is a rabbit, so her 
cackling stump would mean she can stump (as in hit the ground with a 
foot) really loud. See, I have a rabbit who does this a lot so that's 
the first thing came to mind. But my friend seem to think the stump is 
a mere tree stump, and cackling stump is a tree stub that makes noises. 
Then I seem to remember a fair tale about a tree stump (or is it a tree 
branch) that whistles after people told it their secret. So is 
this "Cackling Stump" really a reference to that story?

You help is greatly appreciated!
Java