The federal skilled worker class no longer has a separate stream for PhD students/graduands. However, three options are open to them. I would recommend pursuing the first two, concurrently:
1. Apply to the federal skilled worker class via the new system (called "Express Entry") if you meet the minimum requirements and pass the selection mark of 67/100. Provided that you have excellent English proficiency, which I am sure you do, this would mainly mean having continuously worked for a minimum of 1 year full time (or an equivalent period in part time) in the past 10 years. If you are eligible to apply, you then need to make an online profile, which will assign you a score and enter you into the online pool of prospective applicants. If your score is competitive (depending on the other people in the pool with you), you will receive an invitation to apply. If not, you will remain in the pool until your profile expires (after one year of creating it).
2. Apply to be nominated by the provincial government. There are programs in all provinces for international doctoral graduands. Most provinces ask you to provide a job offer. Ontario and BC do not have this requirement. Google "PNP {name of your province} international phd" to find more information. Once you are nominated by a province, you should still apply to the federal government, but the difference is your chances become almost 100%. If you already have an Express Entry profile when you receive this provincial nomination, your score jumps substantially and you receive an invitation to apply in the next available draw.
3. Stay in Canada and work with your post-graduate work permit. After one year of full-time work, you may apply under the Canadian Experience Class. However, this is similar to the 1st option, in the sense that you need to first apply online and wait to see if you receive an invitation.
I guess still many sept and oct applications are waiting for MR. So let's wait and see.
