My Mother sang this to me when I was little, I sang it to my three children and now my seven grandchildren. It was always followed up by

Me and My Teddy Bear, got no worries got no care.
The words that we sing are as follows
Goodnight Mr Kangaroo, Goodnight, goodnight to you,
Time that little girls and boys sleeping,
Can't you see the great big moon is peeping?
Goodnight Mr Kangaroo, I'm tired of my play with you,
so I'm off to my bed to cover up my head.
Goodnight Mr Kangaroo.

Lullabyes are so special and I always think of my mother when I sing this. I didn't know there was any more to the song than this.