At present you do not meet common-law requirements for Canada which while shorter than the UK still require 1 year cohabitation.
If you marry the application can be submitted for sponsorship immediately, or you can wait the additional three months and apply as common-law.
Sponsorship applications through the UK are fairly quick.
This link provides the timeline for the UK - 7 months for complete packages for the applicant; 89 days for the sponsor:http://www.cic.gc.ca/english/information/times/perm/fc-spouses.asp
Your sponsor must satisfy the requirement that he intends to return to Canada and take up residence here in order to be able to apply to sponsor you from outside Canada.
If you are approved and granted permanent residence from the day you arrive in Canada you are able to work without a permit. As far as working in your field you would need to meet that specific criteria and be licenced.