You are quite right, and I must say I am a bit baffled by the attempts here to discourage you from petitioning the Queen.
There is nothing in Canadian law forbidding a Canadian citizen to make Her Majesty aware of an issue s/he holds dear in respect of the good governance of Canada.
What will most probably happen when you write to the Queen, however, is that your letter will be forwarded to the appropriate Department of the Canadian Government with an instruction from the Queen that this Department supply response to the petitioner as they see fit.
There is evidence, however, to support the belief that the petitions sent through the Queen receive more immediate and quicker attention than those sent directly to the Government. At least, that has been the case in the UK.