Yes, its possible to get PR after 1 year of study. There are different classes to apply as such like CEC, PNP. But the simplest (atleast on paper) is PNP. PNP is a program run by each province. Under PNP, you can apply as an International Graduate (Once you complete your studies). You need to have a permanent full time job offer and thereby worked for minimum 6 months before becoming eligible to file papers for PR.
but its little risky (I do not want to discourage anyone) to go for PR after 1 year of course.
I mean, after completing a 1 year course you are eligible to get one year of Post Graduate Work Permit (which is not renewable). So it mean you have to do "everything" in one year of short time, like
1. First apply for PG Work Permit with in 90 days of your course completion.
(keep in mind it takes minimum 3 months to get the same, and you can't work without having PG Work permit in your hand, however you can apply/search for jobs)
2. To get a permanent full time job
(Considering current economic situation in North America, its may be difficult to get a full time permanent job offer. Its possible but you need lots of networking and valuable skills which are in demand and I have reason to believe that 1 year is a "little short time" to get it done, especially for immigrants. Yes, to make things going on, there are plenty of Part time job options.)
so, why not try for a 2 year course which makes you eligible for a 3 year PGWP ?