My father-in-law is 101 and bits of old songs and poems pop into his head from time to time. He's from England and had a brother in the navy during WWII. Here's his version of the kangaroo song:

my father ate a kangaroo
he gave me the chibbledy bits to chew
when i had chewed them through and through
he gave me more chibbeldy bits to chew

we were hoping to find more verses and the source of this silly silly song