For the early version of the song, http://ddpro.ucoz.com/tpchords/jennifer2.htm has the chords:

JENNIFER'S RABBIT
As sung by Tom Paxton on "Forever Changing: The Golden Age of Elektra Records 1963-1973"

  Em
  Jennifer slept in her little bed
       D                                Em
  With dreams of a rabbit in her little head.
  
  
  Em
  Jennifer's rabbit, brown and white,
  D
  Left the house and went to town one night
   Em                       D
  Along with a turtle and a kangaroo
      Em                         D    Em
  And seventeen monkeys from the city zoo.
  
  
       Am                    Em
  They went for a ride on an old street car;
       D                          Em
  They tried to drive it but they didn't get far.
       Am                  Em
  They all got tired and decided to go
                           D       Em
  To see the people in the picture show.

Jennifer's rabbit, white and brown,
Looked in the windows of the shops downtown.
He found a dress for Jennifer to wear,
And a pretty blue ribbon for her long blonde hair.

Then the rabbit and the turtle and the kangaroo
Bowed to each other like polite folks do.
They went to a shop where the cookies are free,
And they all had cookies and oolong tea.

Then, "My!" said the turtle as the clock struck three,
"The hour is growing very late for me."
"Not at all," said the rabbit, "if you give me a chance,
I'll lead all the monkeys in a hula dance!"

So they danced all night and the moon danced too,
Then the rabbit and the turtle and the kangaroo
Jumped into bed and closed their eyes
And were fast asleep before the sun could rise.

And Jennifer slept in her little bed
With dreams of a rabbit in her little head.