It's difficult to see how it could have been done without a completely different American administration. The British were most vulnerable to attack early in the war, but the American leadership at the outset was poorly suited to any sort of bold move like attacking as well defended a position as Halifax. Their plans were poorly coordinated, underfunded, shoddily executed and their armies were badly led and hamstrung by political infighting. All of those factors conspired to create a totally failed invasion of Upper Canada, where British forces were at their weakest.
The invasion route if Halifax is the target means traveling through the wilderness of Northern Maine, pushing across the Isthmus of Chignecto (which will mean taking Fort Cumberland, the same fort that stymied Eddy's Rebellion), then making it through rough wilderness and hills to approach Halifax. Halifax, it must be noted, had considerable fortifications in place to deter an attack of that kind. It would take a lot of men, and the attacking force would be extremely vulnerable to having its supply-lines and communications disrupted, all while approaching a city that is being continuously reinforced by the British.
Finding a big enough force of men would be a challenge, and not just because the American militia were reluctant to be used as invasion forces. Regardless of any other American goals, securing the west by reinforcing Detroit is essential to hold of Tecumseh and the other Indigenous leaders infuriated by America's pre-war actions. At the same time, the Americans can't really march overland toward Halifax while ignoring the British strength in Montreal and Quebec City. America attacked Upper Canada because the British were weak there and there were large numbers of American settlers they assumed would be sympathetic, but even if they choose to go after the Maritimes instead, they can't afford to ignore the region.
Nor can they launch a naval attack against the concentrated strength of the Royal Navy. Time works against the Americans when it comes to any use of naval assets. The US Navy and their privateers were quite successful in single-ship actions during 1812, but the qualities that won them those successes wouldn't necessarily translate well to an attack against a fortified port. By 1813 and especially into 1814, the naval situation became increasingly grim for the United States. As the location of the Royal Navy dockyard, Halifax is at the centre of that growing strength.
The land that's now part of New Brunswick is less easily defended, but holding it could still be a challenge. Any occupation force would be vulnerable to British reinforcements from either Nova Scotia or from Lower Canada via the St. Lawrence.