Can I post examples of my students’ work on my Queen's learning management systems (Moodle / Desire2Learn / MEdTech etc.) course or on my personal website?
Only if you have the student’s permission. The Report of the Senate Ad Hoc Committee on Intellectual Property states that "the ownership of all types of intellectual property and for all members of the University should rest with the creators, unless other arrangements have been agreed to in advance for certain categories of employment, for certain types of funding, or by individual contract". While the report does outline two possible exceptions to this rule (works for hire, works under contract by the university or by an outside sponser), copyright for the vast majority of student works would belong to the student.
You should always ask students in advance whether they consent to have their work posted online and keep written records of the permissions given.