You should be OK if you stay on the more flat roads which is easy in flat Ohio and Kentucky and stay away from the mountains/steep roads in Eastern Kentucky etc. Most of the Midwest and S.E. is fine for your travels as you have choices of which roads to take that avoid steep grades. It's different in the mountainous states and the East or West coast areas where choices are few and vehicles are driven like maniac controlled missiles in a hurry to go nowhere fast. Just load and drive your rig like it's a big rig as it is for your setup with a 1500 truck with a 5.3 engine but it certainly is capable and can be safely done! It's heavy and will take more distance to stop it!
Also keep your towing below 60 mph max as it's the wind resistance which multiplies at higher speeds that requires the higher HP needed. Even more power is needed to climb "grades" at highway speeds. The rolling resistance is a constant given factor at any speed driven but the wind resistance isn't. You'll be at or n near your max tow capacity with the trailer loaded reasonably and lightly with only a smaller amount of water aboard, 2 adults in the truck with full fuel, etc. Water is heavy whether in the frest water tank or in the holding tanks or both. Why transport it anywhere but just to dump it? Carry a 2 gallon (8 lbs) refillable water container of water for drinking, cooking, etc needs and place it in the shower when traveling so even if it would leak etc, it's not going to get anything wet or soaked. Carrying more dry packaged foods and less quanities of canned goods/liquids really helps also. You can buy a 6 pack of beer, soda, or canned goods anywhere as needed. Your goal will be to think "light packing" and you'll be much happier and safer traveling!
Can you do this? Certainly and do it safely but only you knows your driving habits, your expectations, and what you are comfortable with. Driving below 60 mph lets you drop your tranny down a gear for any grades when needed and you'll climb the grade fine but just slower than the speed limit. Make sure your tires are in good shape and fully inflated on both the truck and trailer and that you are not over any of their max load capacities. Good shocks really help also.