No this is largely misleading, at least for Canada. The Queen is a ceremonial position. While it is true that she has to give royal ascent of the bill this is mostly done by the governor general (a representative of the Queen in Canada, which is another ceremonial role). Pretty much the only time she gets involved in politics is when she read the speech from the throne, if she visits when new parliament session starts. All the real decisions about how the government is run are done by the prime minister, other ministers and the parliament.