Which province in Canada gives PR after 1 year of study?

Yes, it's possible to get PR after 1 year of study. There are different classes to apply as such like CEC, PNP. But the simplest (at least 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 a minimum of 6 months before becoming eligible to file papers for PR.

but it's a 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 means you have to do "everything" in one year of a short time, like

1. First apply for PG Work Permit within 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 the current economic situation in North America, it may be difficult to get a full-time permanent job offer. It's 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.)

Express Entry Stream (Category B) is the most popular stream of NSNP to apply permanent residency in Nova Scotia, Canada. The NSNP EE stream Category has easiest process and it also don't ask the applicant to show any job offer.

Manitoba is known as one of the prairie provinces of Canada and has an economy that is based on an abundance of natural resources and agriculture. It is one of the major contributors towards the growth of the Canadian economy and is also home to the Royal Canadian Mint that produces all of Canada’s coins and currency for 60 governments around the world. The provincial government offers international students the International Education Stream (IES) program within the Manitoba Provincial Nominee Program (MPNP) to allow them to live and work in the province with a PR permit. The IES or International Education Stream is divided further into separate pathways: