I would rename the Dominion of Canada the Kingdom of Canada, as the First Prime Minister; Sir John A. MacDonald, wanted. Unfortunately, the Foreign Minister of the time, and apparently all other Fathers of Confederation were against it:
"On reading the above over, I see that it will convey the impression that the change of title from Kingdom to Dominion was caused by the Duke of Buckingham. This is not so. It was made at the instance of Lord Derby, then foreign minister, who feared the name would wound the sensibilities of the Yankees."
I would also consider calling it "The Great Federation of Canadia.",
"The Imperial Federation of Canadia.", "The Country that Controls the North-West Passage", or even "The Canadian Empire."
The last one would make it more epic when the overpopulated seal herd is sent south to slaughter everyone in the offices of PETA in the name of the Emperor. It would be such delicious irony if PETA was burned down by the very seals they seek to protect.
I would call it Canadia so you could say "ALL HAIL CANADIA!" like "ALL HAIL BRITANNIA!" from Code Geass:
Sorry for taking up so much space.