Final answer:
New Brunswick had achieved responsible government before becoming part of the Dominion of Canada in 1867, a union that maintained ties to the British Crown.
Step-by-step explanation:
Yes, New Brunswick had already achieved responsible government. Responsible government is a system in which executive powers are exercised by ministers who are chosen by and accountable to the elected legislature, rather than the sovereign. New Brunswick attained responsible government in 1854, which preceded its joining of the Dominion of Canada in 1867.
By the time of Confederation, through the British North American Act, New Brunswick, along with Nova Scotia and the Province of Canada (Ontario and Quebec), formed the Dominion of Canada. Although the new Dominion had self-governing authority, it remained part of the British Empire with shared allegiances to the Crown, indicated by Queen Victoria serving as head of state.