Generally it's not the towing capacity that is the problem. It is the payload aka carrying capacity. Look on the driver's door post and see what that number is. The number includes the weight of everything you carry except a tank of gas. All passengers, dogs and stuff. Plus you have to add the weight of a weight distributing hitch and the tongue weight of the trailer.
A rule of thumb is that the tongue weight will be about 15% of a travel trailer which would be 1200 pounds for that 8000 pound TT.
Also on a small SUV you need to worry about what your trailer receiver is rated for. I'm not sure where you will find that but it might be stamped on the receiver or in the vehicle manual. 750 pounds is a number I have heard for these small SUV's in which case you will be severely limited.
You might want to look at popups, which are fine IMO for short trips, or specialty TT like the Trail Manor or HiLo