There is a song sheet, "Battle of Queenstown," in American Memory, but it doesn't have the verse you quoted.
Would you please give the source of your text, and possibly post the words?
The general's name is Van Ransellaer.
The Canadians have a song called "The Battle of Queenston Heights," melody by Alan Mills, apparently never sung. The words supposedly were written in the 1820s. Again, not the same words.

Stan Rogers also wrote a song about the event.