Yep, my family sings this song and my husband thought I made it up. So I did a search and found this!

On a sunset glow, on a bungalow, on a North Australian farm.
A dear little boy and girlie too, were playing with the great fawn kangaroo.
In the evening time when a voice from the darkness said.
You little ones it's time for bed.
You dear little tired and sleepy eyed, the voice from the darkness said.
Goodnight Mr. Kangaroo, goodnight, goodnight to you.
In the evening when the shadows are a creeping.
It's time for little boys and girls for sleeping.
Go away Mr. Kangaroo. We're tired of our play and of you.
We're off to our beds to cover up our heads.
Goodnight Mr. Kangaroo.

At least those are the words my family sings. It may be slightly different than the one you know.