Plus reinforcement schedule right?
This lists the British forces. It's sort of messy but in June 1812 we have:
Upper Canada
41st Foot (Amherstburg and Ft George)
detachment 10th Royal Veteran Battalion (Ft St Joseph I believe. Arrived in Sandwich or Detroit in July or August).
Royal Newfoundland Fencibles [5 companies serving as Marines on the Lakes, but also garrisoning Ft George, York, Kingston] artillery gunners of Holcroft's Company (these would be in garrisons)
Lower Canada
1/8th Foot; 49th Foot; 100th Foot; detachments of the 10th Royal Veteran Battalion and the Royal Newfoundland Fencibles; the Canadian Fencibles and three companies of Royal Artillery.
Maritimes the 2/8th Foot; 98th Foot [part in Bermuda]; 99th Foot; 104th Foot Nova Scotia Fencibles in Newfoundland; and five companies of Royal Artillery.
The reinforcement schedule (if you accept Quebec as being in theatre, which it isn't) is clear from the link:
July 1812 103rd Foot arrives from Ireland
August 1812 1/1st Foot arrives from the West Indies
August 1812 Glengarry Light Infantry Fencibles completes recruiting and is put on establishment. I think in Kingston, but could be York.
October 1812 2/89th Foot arrives from Gibraltar
May 1813 3 squadrons of 19th Light Dragoons
May 1813 2/41st Foot
May 1813 Regiment de Watteville from Cadiz
June 1813 13th foot from West Indies
June 1813 64th foot from Surinam
June 1813 Regiment de Meuron from Malta
November 1813 70th Foot from Ireland
1813 (no month shown) 101st Foot raised
And 1814 is a mess as Wellington's troops show up and go to Plattsburgh.
As to when various units arrive in-theate I can tell the following:
the 49th foot was present at Detroit in the middle of August 1812 so it was clearly dispatched to Upper Canada immediately.
I'm pretty sure that 1/8th came up the St Lawrence with Prevost in winter 1812-1813. The 100th foot seems to have stayed in Lower Canada until early 1813. The 104th foot performed a heroic winter march to Quebec and arrived in march 1813, but only a few companies seem to have served in Upper Canada in 1813. In 1814 the whole battalion was in theater. The 103rd doesn't seem to show up in Upper Canada until 1814. 2/89th seems to have had one company on the Niagara front in 1813, in 1814 the entire battalion was in Upper Canada. The 1/1st was in action around Lake Ontario in 1813. The 2/41st was sent straight up to Upper Canada upon arrival in Quebec in 1813 as were the three squadrons of the 19th dragoons. The De Watteville Swiss regiment came to Upper Canada in 1814 as did the second Royal Marine Battalion.
I think that these are all the troops that served in Upper Canada through 1814. The Canadian Canadian Voltigeurs were active between Montreal and Kingston, but were based in Montreal. There were also incorporated militia and (obviously) the militia themselves.