General information about the whole process of getting a license is provided below. http://www.peo.on.ca/index.php/ci_id/2057/la_id/1.htm
You might be eligible for applying to full license from the beginning, but I prefer enrolling as EIT (Engineering In Training) first, which might have same application form but less fee. EIT link: http://www.peo.on.ca/index.php/ci_id/2064.htm
In any case, I recommend to apply sooner than later as your application fee might be exempted if graduated within 6-months from a Canadian University. http://www.peo.on.ca/index.php/ci_id/2063/la_id/1.htm
Then you will be in the process and can register in LAP program with any guide. LAP makes a pairing of PEO license holder and EIT (just like mentorship program). http://www.peo.on.ca/index.php/ci_id/2010/la_id/1.htm
To become a volunteer in PEO, one has to be either P.Eng. or EIT. There are some committees/chapters which have EIT representatives. http://peo.on.ca/index.php/ci_id/1850/la_id/1.htm
It might take any body 2-3 years to complete the whole process (of becoming P.Eng.), because most of the stuff is still manual (paper based) and each persons eligibility is different.
project management qualification
Project Management: Normally the project management field is all together different area and doesn't require any prior qualification, but in North America one needs a PMP (Professional Management Professional) certification to be formally recognised.
PMP certification has its own requirements, and might take at least 6-12 months (after eligibity is met) to prepare for the exam, that all depends upon your previous knowledge of this field.
The whole PMP-certification process can be found at PMI website: http://www.pmi.org/
If you want to have a flavor of this subject you can always enrol at UoW- Professional Development courses http://pd.uwaterloo.ca/onlineprojectmanagement.html
These are easy to manage (online), not expensive, less time consuming (4-6hrs/course/week) and you can register one course/semester with no long term commitment. Other advantage: They are counted towards PDU requirements for PMP application (if you intend to do in future).