As i'm sure you may have noticed, although David claims to be a member of Mensa, he doesn't appear to be very well informed. In fact, Canada is a confederation, which assembled itself gradually between 1867 and 1949. David's confusion probably arises from his stupid assumption that any nation which is not like the United States isn't legitimate. David gives the already disreputable term "American exceptionalism" a worse reputation than it deserves.
A republic is a nation which is governed by laws. It doesn't mean anything else--it doesn't mean democracy, it doesn't mean a written constitution, it doesn't specify legislative or executive institutions or processes--it just means a nation which is governed by laws. The states of the United States are not republics in the sense of distinct nations--although that is what state meant before they formed a federal union. The United States constitution guarantees a republican form of government in all states--and once again, that has absolutely no implications for democracy, legislative and executive processes, etc., etc. It just means that each and every state will be governed by law.
Canada was, prior to July 1, 1867, simply the two provinces of Canada East (Québec) and Canada West (Ontario), and was a conjoined imperial province of the British Empire. In 1866, Fenians (Irish Republicans, who in at least one case carried a flag emblazoned "I.R.A.") who were veterans of the American Civil War, invaded or attempted to invade Canada at several points. Most of them were rounded up before the fact, or turned back by American Federal agents or the United States Navy (they were crossing the Great Lakes), but one group made it into the Niagara peninsula, and marched toward Ridgeway, Canada West, near the site of the biggest battle between the English and the Americans during the War of 1812. Several overconfident militia units, quite a few hubristic and incompetent militia officers, and the Queens Own Rifles (Toronto), marched out, and were routed by, thoroughly humiliated by the Irishmen, who were combat veterans with years of experience. The Irish then marched back to Fort Erie, retook it from the Canadian militia, and then surrendered to the United States Navy in the Niagara River, because Colonel O'Neill had fulfilled his mission, which was only ever intended to be diversionary.
The Canadians had been feeding the national vanity on a ridiculous myth dating from the defeat of an American invasion in December, 1812, first publicly articulated by the Anglican Bishop Strachan of York (later Toronto), which claimed that the Canadians had defeated the Americans almost single-handed, and that the English could not have fought and prevailed in Upper Canada (what Ontario was then called) without them. It was bullshit, as historical myths usually are, but it was based on even less truth than most historical myths are. Ridgeway in 1866 made this starkly clear, when thousands of Canadians were outmarched, outfought and routed by a few hundred Irish veterans of the War Between the States.
The English were now more than happy to drop them like a hot rock, because they certainly weren't prepared to spend the money to protect the Canadians indefinitely from invasion. (There are Canadians to this day who believe that Americans cherish a desire to invade Canada . . . yeah . . . right . . . as if . . . ) They quietly and in no uncertain terms let the Canadians know that they needed to take care of themselves.
Two adroit leaders--one each from Canada East and Canada West, who already had a parliament of their own, and had worked out the deals for French-speaking Catholics and English-speaking Protestants who cordially and openly despised one another to live and work together--began to work on creating an independent dominion within the empire. There was at that time a meeting of representatives from the Maritimes (Nova Scotia, New Brunswick and Prince Edward Island) who were meeting in Charlottetown, PEI. They had been screwing around over the idea of a Maritime Union for years, so MacDonald and Cartier from Canada took their show on the road, and the result was the confederation which became the Dominion of Canada as of July 1, 1867, with the Maritimes joining the two Canadas. Manitoba was stolen, fair and square from the inhabitants, and over the next several years, British Columbia, Alberta and Saskatchewan joined up, and the English turned over their other major North American territories to the Canadian Dominion.
In 1949, the die hards of Labrador and Newfoundland finally said: "OK, eh? We'll join, get off our backs." The Queen gave the Canadians the British North American Act sometime in the 1980s (?)--Canada had already ceased to be a Dominion in 1967. You can bet David doesn't have a clue about any of this. By definition, Canada is a republic, although many Canadians don't even understand that.
Never listen to an American conservative: not only do they usually not know **** about history or the rest of the world, they usually even show a profound ignorance of their own nation's history and constitution.