Tow a U-Haul trailer with a Civic?

One rental company estimates you would need a 10’ truck and a tow dolly. $2000 + fuel.
We recently moved from New England to the South West. After estimating the cost of a renting a truck or using Pods I found that a moving company was best, not necessarily the cheapest but close enough. We packed, they loaded, delivered and unloaded. In your situation I would suggest you get an estimate from a motor freight carrier. You box and load they deliver. Drive the Honda.