The simple reality that we can see from 1838 and 1866 is that the assumption that volunteers could be raised rapidly (and that like OTL much of the early mobilization would be entirely organic) is completely correct, and with British help they can be armed and equipped and put in defences to deter serious assault in good time.
Of course the difference ITTL is that the border tensions have been ongoing since October, the militia has been called out since the end of the same month, the British have responded in kind by ferrying more troops and arms over in November than historically, and the organic meeting of volunteer and sedentary militia companies is taking place much earlier that OTL.
When they go to call the militia out earlier here there's going to be a nucleus of volunteers which will rally to the flag. The creation of new battalions would be a rather simple affair if going by the scheme proposed by the commissioners historically, and that which was adopted when they were rapidly created in 1864 and 1866.
As to staff and officers, well there wasn't a shortage of qualified officers assigned to the task historically, nor was there lacking any men inside Canada who could fill the necessary shoes there.
But I'm getting ahead of myself
Like who? Of the staff charged with planning deployments and a defensive response only MacDougall believed that the US could overcome the major disadvantages of winter to move forces north. Even then these hypotheticals were still in line with the belief that the US would make peace with the South to take on Britain alone, considering it would the height of folly to do otherwise.
Otherwise there's little pessimism in the prospect of taking on the North, and when one views the various responses by each side historically, they have a point. Wolseley wrote that 'it would be a toughish work' but felt it was doable after all.
There's no doubt the political will was there by December as Palmerston told the Queen "
Great Britain, is in a better state than at any former time to inflict a severe blow upon and to read a lesson to the United States which will not soon be forgotten." and even Lewis as the new Secretary of War certainly didn't seem especially pessimistic as preparations wore on writing "
we shall soon iron the smile out of their face" (emphasis original).
Then of course on the whole subject of war one eminent historian has written: "
Thus the British must always have been confident of ultimate victory, provided that the Americans remained so dependent on their trade and shipping and their naval power did not rival Great Britain's. There was much that would have made them hesitate before going to war but in the end only the danger of betrayal by a European neighbour would have been a really effective deterrent. Once this had been removed-as it was in the Trent case-then the British were prepared to accept the cost of an Anglo-American war, even humiliating though temporary defeat in Canada, rather than sacrifice their prestige as a great power by headlong diplomatic defeat."