There is no standard answer to "Can I tow this?", all depends on how many people, how much stuff you plan to carry, how close you may be to any of your ratings.
Your tow vehicle has multiple weight ratings. The 8100 lb tow rating is just one of them. The vehicle also has a "max occupant / cargo weight" rating (AKA payload), the tires have both a speed and weight rating, the axles have weight ratings, and the hitch receiver has one rating for carrying dead weight (without weight distribution) and another rating for when weight distributing is applied. True towing capacity is limited to the weakest link in the vehicles overall ratings. Normally, that weak link is payload.
Trailer tongue weight and weight of added hitch / sway equipment are counted as cargo weight in / on the tow vehicle. Your tow vehicle needs a payload capacity to carry the combined weight of everything / everybody you put in or on it, plus the tongue / hitch weight.
Trailer tongue weight is not a constant number, it fluctuates up and down during every trip. Average is 12 - 13 percent of whatever the loaded trailer weight happens to be. Depending on how the trailer is loaded and location (in relation to it's axles) of it's holding tanks, tongue weight can be 15 - 16 percent. Less than ten percent can cause sway issues.
Weight distributing hitches have two purposes. The primary purpose is to restore lost weight (caused by trailer tongue weight) on the tow vehicle's front axle, and secondary purpose is leveling the tow vehicle / trailer combination.
Average trailer load (dishes, pots and pans, bedding, BBQ stuff, camp chairs, groceries, water, etc) is 800 - 1000 lbs. With 4500 lbs dry weight, you will be over 5000 lbs, loaded. I would say yes to the distributing hitch. Also note the weight ratings on your receiver hitch, it most likely will tell you weight distributing is required for tongue weight in excess of 500 lbs.
You'll find a tire / loading sticker on the drivers door post. It will have a number for "max occupant / cargo weight. That's the payload you have to work with. Your trailer will use about 800 lbs of that carrying capacity. If the bicycles and stuff create an issue with your payload, you could move some into the trailer.