You have to look into what immigration class you might qualify under. According to
http://www.cic.gc.ca/english/immigrate/skilled/apply-who-instructions.asp#list you would not be able to apply as a skilled worker unless you have a job offer. Most provincial nominee programs also need a job offer. Quebec skilled worker doesn't need a job offer but is your gf in Quebec? If not, it would not make sense to apply there.
If you go to Canada as a visitor, you could see if you can get a job offer. If you get one, as an accountant, it should not be hard for you to get a 3 year work permit under NAFTA, see
http://www.canadavisa.com/nafta-temporary-work-permit-canada.html During that time, you would qualify as common law partners and your gf could sponsor you. Through spousal sponsorship through the US, you should have your PR in no more than a year. The employer could also sponsor you through a provincial nominee program.