Alternatively, if you are eligible to apply for permanent residence under the CEC class (after 1 year of full-time employment), you could submit your PR application. (This would require a letter of employment from your current employer).
http://www.cic.gc.ca/english/immigrate/cec/index.asp
After you submit your complete application (it does take some time to put together a complete application), you would receive an "acknowledgement of receipt" (approximately 2 months), you would be eligible to apply for a one year "bridging open work permit". An open work permit allows you to work for any employer. And of course, if you were successful with the PR application, then you could work for whomever you want, for however long you want.