Classically speaking, I think Tooth Fairies were a race of fae, not an individual like say Santa Claus. Though I think they were also more sinister (tooth trolls), so it may or may not apply. Given that she was bound to somebody else's service before Harry, Im guessing there is no conflict of responsibility, either she can get away enough to accomplish it or there are others to take up the slack. In fact, I think Winter Law and/or Fairy Nature would require her to, Harry doesnt have the power to make her break previously standing oaths.