I was singing the song to myself this morning and found I sang "So off she went, just as fast as she could run" instead of "She ran to the shop as fast as she could run". Then if you say "she got him a coat [etc]" instead of "she bought ...", she could have begged, stole or borrowed the item too. I have also heard versions where "off she went to her grandfather's chest, and she got him a coat of the very, very best." I see that line appears in versions given by Peg and sophocleese.