I cant answer for certain, but its possible. All Provinces have a full reciprocal agreement with one another, so they share conviction information, etc. So in your case the seatbelt ticket you got in Quebec will show up on your Ontario abstract, with the appropriate demerit points applied. Im not sure if that suspension can be carried over to your Ontario licence as well, but I believe it can.
Section 198 of the HTA deals with this:
Licence suspended for failure to pay judgment
198. (1) The drivers licence of every person who fails to satisfy a judgment rendered against him or her by any court in Ontario that has become final by affirmation on appeal or by expiry without appeal of the time allowed for appeal, for damages on account of injury to or the death of any person, or on account of damage to property, occasioned by a motor vehicle or street car, within fifteen days from the date upon which the judgment became final shall be suspended by the Registrar upon receiving a certificate of the final judgment from the court in which the same is rendered and after fifteen days notice has been sent to the person of intention to suspend his or her licence unless the judgment is satisfied within the period, and shall remain so suspended and shall not at any time thereafter be renewed, nor shall any new drivers licence be thereafter issued to the person, until the judgment is satisfied or discharged, otherwise than by a discharge in bankruptcy, to the extent of the minimum limits of liability required by the Insurance Act in respect of motor vehicle liability policies.
Reciprocal effect of subs. (1) with states having similar legislation
and (4) The Lieutenant Governor in Council, upon the report of the Minister that a province or state has enacted legislation similar in effect to subsection (1) and that the legislation extends and applies to judgments rendered and become final against residents of that province or state by any court of competent jurisdiction in Ontario, may declare that subsection (1) shall extend and apply to judgments rendered and become final against residents of Ontario by any court of competent jurisdiction in the province or state.
It may take some time for them to actually process the suspension request in Ontario, so I would look into dealing with the Quebec ticket asap to avoid any type of suspension history on your record.