This is a pretty good example of why the use the gvwr of the trailer as the actual weight isn't always the best estimate. The trailer this guy is looking at has over 4000 lbs of carrying capacity, some other travel trailers have only around 1200 lbs. So the theory goes that since he can load 4k he will, my guess is he won't. If he loads a 1000 lbs in it then he will be at 8k. He will have plenty of engine for it but will probably be over on payload by a few hundred. but I doubt he will be exceeding the gross axle weight ratings of either axle. Will this trailer put the truck over some? Probably. I guess it comes down to what someone is comfortable with. A 3/4 ton truck would be better for this trailer or a smaller trailer would be better for you but I can guarantee people drive happily down the road with a similar setup every day.
If you decide to go ahead with the trailer lt load range d or e tires and airbags will probably make it work better for you but it will still be over the factory ratings. Like I said plenty of engine but you will be coming up short on payload.
If I were you I would probably look for something about 1000 or so pounds lighter that will end up closer to 7k loaded. Whatever you get make sure you have a proper weight distributing hitch and some kind of sway control.