We'd change our constitution.
With the information about the voting process added to this consideration (changing the constitution), it hardly seems worth the effort to change to a Republic.
Australians already are free, yet wear Brazil's colors for civic and athletic events, pay other countries to take in the refugees they don't want, and can't find a missing airplane 'with both hands,' as the expression goes. So why bother? The only reason would be for the sake of acquiring some measure of national pride. That's different from the motivations of the people of Catalonia, Scotland, and some other areas around the world where there are independence movements underway.