Gosh, don’t suggest it. Nobody here notices the constitution, and the term “Commonwealth of” is unknown except to pedants, lawyers, politicians and cranks. But if you suggest that other countries might notice words in some arcane document nobody has ever read, then you’re hitting a sore spot.
“Other countries might think” is a strong argument in Aus. Like Motherhood, Apple Pie, and The American Way.
I honestly don’t know whether “confederation” was used at the time, or not. The preamble to our constitution mentions the word “Dominion” once, and “union” a few times, but not “confederation.” The would-become Canadians and the British were certainly aware of the US Civil War, which is why the drafters of the British North America Act 1867 (Canada’s constitution) took care to enumerate which powers were federal and which were provincial–one of the disagreements that the Confederate states and the Union were fighting over.
I can say that “confederation” is a term that we Canadians grow up with. I do remember Canada’s 100th birthday in 1967–I was a child at school, and we were encouraged to do some sort of “confederation project.” High school history classes mentioned confederation as synonymous with July 1, 1867, and subsequent university classes did as well. The term was used a lot again in 2017, for Canada’s 150th birthday. So if it wasn’t used in 1867, I’d like to know when it started to be used. You have a good question, and now, I’d like to know the answer to it too.
For example, the Parliament of the Province of Canada debated the Quebec Resolutions, ultimately voting in favour of them. The debates were printed in their entirety: Parliamentary Debates on the Subject of Confederation of the British North American Provinces, 3rd Session, 8th Provincial Parliament of Canada (Quebec: Hunter, Rose, 1865).