New to RV and buy my first RV

Pretty close to my set up, mine is 5400lbs empty and I only have the 4spd tranny but with 3.73. No problems at all tows great.

That is fairly similar to my setup. I've not encountered many issues, although you won't be setting any land speed records. I think Chevy has started having a decent brake controller which can work with the vehicle's computer which can use the trailer brakes to prevent sway. If you have that and a good transmission cooler, as well as a decent W/D hitch, you should be good to go. Expect 5-6 MPG so try to stop to get gas every 50-75 miles just to be on the safe side.

I'd also recommend carrying a couple 5 gallon cans of gas in the bed. I do this mainly for the generator, but if you are really stuck for fuel, it will buy you an extra 20-40 miles.

You should be good to go. You may not set any speed records going up hills and mountains but just take it easy and enjoy the trip.

Fill it and go weigh it. Funny how they gain weight.

The weak link on a 1/2 ton tends to be payload. Go look at your drivers side door jam and look at the tire loading sticker where it will say "occupants and cargo should not exceed x lbs". Now subtract the weight of everyone and everything that will be in the truck when towing. that new number is your available payload. the loaded Tongue weight must be less than this number. loaded tongue weight should be 13-15% of loaded TT weight. An even more accurate way to approach that is to go weigh your truck loaded ready to tow with all passengers, pets and gear that will be in it when towing plus a full tank of fuel. Take the scaled weight and subtract it from TV gvwr to get available payload. Take the scaled weight and subtract it from gcwr to get adjusted towing capacity. You need to stay within all these weights.

The TT you list, gives a 5272 lb dry weight and a gvwr of 7000 lbs. Most tend to add 1000-1500 lbs to their TT. Some mee, some less. With that low of a cargo capacity, I would do your calculations using the TT gvwr. For 7000 lbs you are looking at a potential tongue weight of 910-1050 lbs.