The US have no concept of a constitutional monarchy so the importance of the two key issues here are lost on them.

By constitutional convention if Harper had lost a vote of confidence (or equivalent) he would have been obliged to resign as prime minister.   That bit most people seem to have got.

The sovereign (in the case of Canada, by her proxy the Governor General) in exercise of a residual power would then have appointed the next prime minister. Probably the most followed view amongst constitutional lawyers is that that should be the person best able to form a government, ie the person best able to command a parliamentary majority. Whether that should be the next leader of a fallen minority government party (ie another Conservative in place of Harper) or the person designated by a larger coalition is an issue the jury is out on but IMHO the better view favours the latter. This (or a closely related subject) has been a live issue in England twice and there is still no definite answer.

The really exciting point is the prorogation. Technically the Queen prorogues parliament, and does so on the advice of her prime minister - but it is very open to argument whether that should be what happens when the sole real purpose is to avoid a vote of confidence. Since Prime ministers may call general elections (again theoretically by so advising the crown) at times to suit themselves, I suspect that there is yet no convention that prorogation cannot be effected for party political purposes. But I might be wrong on that.