Nick, I disagree with most everyone. In Europe even smaller cars tow more then what you have in store.
Is it an automatic? If so just monitor the color/smell of the tranny fluid when you get there and get back. You might have to change it sooner then expected, but that's the only nit here.
I towed a 1,000+ lb trailer with my 2007 Toyota Yaris from Seattle to Nashville with no incident, nor handling issues. My Yaris has a 1.5L but less power then your Cruze, and it is a bit smaller car too. Sure it had less get up but it was not so bad that it was dangerous to get on freeways. I checked the auto-tranny fluid upon arriving in Nashville and it was a tad darker then expected, so instead of changing it out at 50,000 miles, I'll do it at 40,000, which means I have 10,000 to go since the last change.
The trailer I was pulling was filled to the gills, and was longer then my car. and the car was filled with stuff to the point of nearly bursting open. During the trip to Nashville, we got a lot of strange stares, and often these lookers would laugh in disbelief! We averaged 75 MPH that trip, but our MPG dropped from a usual 40 to 21 MPG.
We towed that same trail on another trip; from Minneapolis to Seattle a year before, and we had to climb over a few mountain ranges such as the cascades, with no problems, no handling issues.
The only big difference is that my car was made in Japan, which means it is nearly indestructable; can't speak to that for your Cruze however.
My car has over 136,000 miles and I have spent $0.00 on repairs. It runs perfectly today.