I see that you posted this quite awhile ago but I do remember my mom singing that to me all the time. I was born in 1956. These are the words I know -

Spacey the Runaway Robot lived way up on the moon.
He took a little trip on his daddy's rocket ship and off he zoomed all way to the moon.
Zoom, zoom, zoom through space he zoomed. He didn't need a pilot and he didn't need a broom

Gosh, now I can't remember the rest. I wish I knew where it came from. I Googled it to find out and nothing, but that's how I found your question. Good Luck!