Good morning, my name is*****'m a Canadian lawyer, and I'd be pleased to help you with this question.
In general there are not barriers to moving between provinces in Canada. You do have to change documents such as a driver's license over to the new province, but this is not all that difficult, though it may involve some time spent waiting in various government offices.
In the year after you move, you would need to do two provincial tax returns January -- move month as a Quebec tax payer, and move month to December as an Ontario tax payer. But that's something you'd only need to do once, and there are organizations in Ontario that offer free assistance in completing tax returns to seniors, if you decided you wanted help.
The primary draw back is that you need to change your Health Insurance from the Quebec plan to OHIP. You will need to reside in Ontario for three months before you are eligible for OHIP, and during that time if you need medical care it would be charged to the Quebec health plan. This may involve prepayment, or waiting for Quebec to authorize the medical treatment as Quebec and Ontario do not have reciprocal medical plans. There is more information on this waiting period here: http://www.health.gov.on.ca/en/public/publications/ohip/ohip_waiting_pd.aspx
There are exceptions to the general rules regarding OHIP, and I can look into those to see if you might qualify for a shorter waiting period (or no wait at all) but I couldn't give you the results of that research until later this afternoon.
If you have specific questions about other things you might need to change, please let me know, and I will look into those as well. Of course, if I have fully answered your question and you do not need me to do further research, kindly provide me a positive rating so I can receive credit for my answer.
My answer here contains only general legal information and not legal advice. No solicitor/client relationship has been created by this communication.