Quebec voted to eliminate its upper house a few years back. So it can be done.
Unanimous consent is childish, it is a sign of an immature political culture because it smacks of inequality and privilege. Which is what the Senate and Crown are. "My work is special, no one can change it."
Of course it can be done.
When the Parliament of Québec abolished the Legislative Council, this was through a simple amendment to the provincial constitution. The process for the abolition of the Senate would be a much more comprehensive one, and would require the consent of the Senate, the House of Commons, and all ten provincial legislatures. This is not childish at all—rather, it is to ensure that the Canadian people's regional interests are defended.