Just use common sense and you’ll be fine. What you will discover is that you will not even notice that trailer and car is there. It’s a piece of cake.
Obey the speed limit, use care in traffic because a heavy load requires more stopping distance, and the most important of all; just don’t cut corners. You will need to swing out a bit.
I went with my son a few years ago and helped him when he moved up to Colorado. His wife drove one car and we went in a 24 foot U-Haul with an attached trailer with car on it and had no problems even with one that size.
As mentioned, backing up can be a pain for the inexperienced.
What I would suggest is that when you arrive in your general area that you stop in a parking lot and unload the car. Take the trailer, drop it off at the U-Haul office, and then drive the truck to the destination for unloading. Makes it much simpler by eliminating that trailer as quickly as possible.
After a 100 miles behind the wheel it will all become second nature. Enjoy your trip.