Although the Queen of Britain is Canada's head of state, our "representative to the world", she does not actually have any powers in Canada. All control was long ago delegated to the Governor General and the Prime Minister. The Governor General is appointed by the Prime Minister, or rather, the Queen appoints the Governor General on the advice of the PM (the Queen has never disregarded Prime Ministerial advice in making the appointment). The Governor General is supposed to act as a "representative of the Queen" instead of the representative of the Canadian people, and this is why the current office of head of state is unacceptable.
Under a republic, the head of state's role would be to represent Canadians and not the British empire or the Queen of Britain. Since Canada is a republic in all but name and head of state, the changes would likely be minimal. Although there is a proportion that favors the American Presidential system to our Parliamentary system, they are a minority. Likewise, other reforms, either for changes in the electoral system or in the senate will likely take place outside of the change to a republican system of government. The reason behind this is to avoid divisions from within a republican movement over other reforms.
Parliamentary republics with a head of government (PrimeMinister), and symbolic President outnumber the Presidential republics in the developed world. The Presidential republic is based on the American system with a merged executive of President that is both head of state and head of the government. Germany and Ireland are both examples of Parliamentary republics with separate offices for head of state and head of government. For Canada to become a Parliamentary republic, all that is needed is to change the role of the current head of state, the Governor General. The minimalist reform is to simply change the written responsibility of the Governor General representing the Queen, to a President representing the Canadian public. In this case, the President would have the same duties and powers as our present Governor General, and continue to be appointed by the Prime Minister. Other options are to have the same kind of President as the one outlined above, only appointed by Parliament, the Senate, the Supreme Court, or by national popular vote. In all options, the President would continue to hold the same powers as our current Governor General.