Years ago, before I had a truck, I drove a Jeep Cherokee. When I killed my first ever deer, I loaded it onto a trailer and drove to a friends house because I had never butchered one before.
A year or so later I killed a button buck on public land and threw it on top of the Cherokee. Tied it on there with 550 cord and drove 40 miles home. I have a buddy who drives a jeep and uses one of those little tow hitch platforms for his deer. You do what you have to do. I've even seen guys out there in sedans who kill it on site, and butcher it there, placing the meat in a cooler. Don't know how they handled the tagging, checking of it but I will give them the benefit of the doubt. The guys I have seen had heavy plastic bags for the carcass but I know that doesn't always happen and sometimes folks just drag the bones into the woods. I've never seen that happen and don't approve.
Towing it should be fine. Just make sure you lock your trailer. thieves are stealing anything metal these days.