OK, I just watched the video again and found that the chords I posted above were completely wrong. Sorry for that! I've posted the correct chords on my website here:
Jennifer slept in her little bed
G E Am
With dreams of a rabbit in her little head.
Jennifer's rabbit, brown and white,
Left the house and ran away one night
Along with the turtle and a kangaroo
And seventeen monkeys from the city zoo,
And Jennifer too.
They ran through the forest and they all held hands.
They came to the ocean with the cookie crumb sands.
Called it the sea of the very best dreams,
And they all built a castle of the best moon beams.
And milky way streams.
Song is actually in D minor - capo on 5th fret. But that doesn't matter. Tom ends the song with a beautiful A major chord.