Never cover your car once you put it on a trailer. Never. Never ever. Don’t do this (unless there is no paint on your car).
Paint doesn’t heal, and your car’s paint can only handle so much massage. And going down the road the cover becomes a mild abrasive, and will rub your paint until there ain’t none left.
So while you have great intent, covering a moving car is about the worst thing you can do. And when you get to your destination, you might just find that the paint is irreparably damaged.
This is a red Bugeye that came to visit, and came covered. You might be able to see the “over-buffing” on the top edge. The cover literally scratches the paint and wears it thin. Even a fleece lined cover is at risk of doing the same. When an enclosed trailer is not an option, no car cover but a tonneau cover installed and zipped is best.