I don't know it as a song, but the longer saying I heard was:
Dance like no one is watching,
Love like you'll never be hurt,
Sing like no one is listening
and live like it's heaven on earth!

A Google search turns up that it's by —William Purkey.

I also turned up an Irish proverb:
Work like you don't need the money;
dance like no one is watching;
sing like no one is listening;
love like you've never been hurt;
and live every day as if it were your last.