The original poster was asking for safe transport within Canada. Most US transporters do not operate in Canada.
Here are two Canadian company I recommend. Both are great, but not cheap. But, why be cheap when it comes to transporting something that is important to you??
https://www.thorsonsevt.com/
http://www.mackietransportation.com/...-transport.php
I transport a lot of cars and my clients transport a lot of cars. Within the US, use the big guys like Reliable, InterCity Lines, Passport, etc. They got the right rigs and have tracking for all of their trucks. They will insure your car and provide proof of insurance. If you do use a smaller company or individual, make sure you see PROOF that they have insurance. Not just insurance for their truck and trailer, but insurance for YOUR car as well.
You've spent a lot for your car, don't be cheap on transport.