The version my Grandad (born circa 1900) used to sing to us in NW England in the 1960s went:

When the golden moon comes a peeping, soon, Mr Kangaroo with pride
Creeps up to the door of the bungalow
And he won't go away, oh no oh no,
From his playmate's side.

From the trees a voice calls out,
'You little ones it's time for bed'
So three little tired and sleepy heads
to the kangaroo then said...

Goodnight, Mr Kangaroo,
Goodnight, good night to you,
Now that evening shadows are a creeping,
It's time that little boys and girls were sleeping

Goodnight Mr Kangaroo,
We're tired of our play and you,
We're off to our beds, to lay down our heads,
Goodnight Mr Kangaroo.