Easy Google search shows this car should not be pulling a travel trailer.

Motorcycle trailer, sure. But basically best case scenario this trailer is at it's tow capacity, which does not give much wiggle room for failure.

But most likely it's quite past the tow capacity. It's tow capacity is 2000kg/4400lbs. A travel trailer's dry weight is already close to that. If it was a pop up camper that'd be one thing, but this is a full dead ass travel trailer. It's probably around 5000lbs, and who knows what's stuffed in the back. This is a safety issue.

Quick edit: this is not to say you need to own an F150 for the one time a year you do this, but maybe rental?