Refer to the eligibility criteria for FSWP in the following link:
http://www.cic.gc.ca/english/immigrate/skilled/apply-who.asp
Even if you have a job offer with a positive AEO, you would still need to fulfill the other minimum requirements and meet the minimum of 67 points to apply for FSW. That means, yes, you still need to have at least one year of experience in a skilled occupation.