Marsh, This was a favourite at Girls' Brigade Camp in Scotland in the dim and distant days of my youth!! We used to sing it with the appropriate actions. My version is very similar to yours:

Little cottage in a wood, Little man at the window stood, Saw a rabbit running by, Knocking at the door, Help me! Help me! Help me! he said, Or the hunters will shoot me dead, Come little rabbit, come with me, Happy we shall be!

We only had the one verse.

Anne