Our group of four gamed this interesting battle through the Fall and replayed it (switching sides) and modifying the start to start the game when the American forces have the heights.
We used General de Brigade rules with an addendum of rules to cover War of 1812 issues such interplay of Indians and use of boats etc. I have British Grenadier as has been commented on. They are a good set of rules however, I don't like the concept and tracking (or any kind of record keeping) of Disruptions Points. I was hoping that there would be more on Indian tactics and rules but sadly this not the case. I really like G de B as the rules are a balance between realism and fast play and they are geared to division level game that fits most War of 1812 battles.
The figures we used are:
Knuckleduster: superb sculpts, most extensive range (particularly Americans and Canadians plus many unique figures)of all figure manufacturers, compatible with Perry, Front Rank, OG and Victrix. Usually purchased in groups of 4 to 6 at USD1.66 per figure with options to purchase battalions of 24 figs at a discount. They are the only company that produces accurate Indian uniforms for the tribes that fought during the War of 1812. KD also produces a unit builder guide that list units and the suggested figures that wold best replicate it. A very useful tool.
Old Glory: Very nice castings, a good range (British, Americans and some Canadians), compatible with P, FR, OG and KD. The best value in bags of $30 infantry for $35, about $1.17 per figure.
Foundry: very nice castings, did have a good range including Americans and few Canadians but the availability has been reduced. These are smaller 28mm castings that are not compatible with P, FR, VX and KD. I have used some F with OG units and they look fine. They used to be expensive but are recently reduced to $12 for an 8 pack which is 1.50 per figure.
Matchlock 28mm (part of Minifigs): good castings but a limited range of Americans. They are compatible with P, FR, VX and KD. I would not mix them with Foundry but the one or two figures will mix with OG. They are approx $1.82 per figure.
Brigade Games 28mm: they are just starting there War of 1812 range with late war (1814) American Infantry, gray coated Infantry of Scott's Brigade and artillery crews. Three selections; command, marching and skirmishing. Compatible with P, FR, VX, OG and KD. These are really exquisite sculpts that are a joy to paint. A little expensive but worth it at $2.00 per figure in bags of six.
If I had only one choice it would have to be Knuckleduster; the most extensive range that is continually expanding with superb accurate figures at a reasonable price.
If have any further questions don't hesitate to ask. It is always nice to see more War of 1812 gamers. BTW here is a link to the final moves of group's many posts on the Battle of Queenston Heights;
http://kangarooblogger.blogspot.ca/search?updated-min=2014-01-01T00:00:00-08:00&updated-max=2015-01-01T00:00:00-08:00&max-results=4