If you need to move any serious amount of stuff, you shouldn’t even try it with the Civic. If you’ve never towed before, I also recommend against a dolly, and put out a vote for a proper car trailer. You can even tow that behind a pick-up, if you like, and still store stuff inside the Civic for a bit more room.
I moved from FL to ND this way, towing our Jetta behind our 4Runner (V6, no less). Not one problem, and we took a lot of stuff with us…enough to live on for 3 months until we found a house and had our real “stuff” delivered. As my wife works in Human Resources and I’m in IT, we both need lots of nice clothes, and I also took some computers with me so I had both toys and tools for the trade with me. Plus, if you’re moving, there are things the moving companies won’t move for you. I had to tote those myself.
My wife still likes to say she has “1800 air miles” on the car.