Disco 2 is rated for 7000lbs+ towing capacity...I have a 19' camper in the 4500-5000lb range. Am I going to run into any problems?

I have break assist and anti-sway tow hitch.

 

Big hills won't be fun since these things are underpowered, and I really hope you have trailer brakes. Other than that, you should be good to go.
Tow rating is 7700, but only in low range. High range limit is 5500. No brakes limit is 1650! And off road limit is 650.

I've towed 4500 on a braked trailer (Uhaul) with my '03 D2 with no issues aside from it being painfully slow on big hills.

 

it's going to be slow and unless you have airbags in the rear suspension, your going to have some rear sag with the Discovery nose being ever so slightly up in the air.

 

My first Discovery was an '03. I towed a big box trailer once when I had about 160k miles on the clock. The trailer with cargo was probably about 4,00lbs. The Disco did ok but it worked really hard to keep highway speeds. This is anecdotal at best, but after I unhitched and started the engine again there was a nasty clatter. It had slipped three cylinder liners without an overheating event. Not saying it would happen to you, but that's when my otherwise reliable Disco died.

The anti-sway bars should help a lot because the rear suspension is kind of soft. The Discovery has a 1,488lb payload capacity which includes the entire contents of the vehicle as well as the tongue weight of the trailer. The tongue weight of your trailer (if properly loaded) will be 10 - 15% of the trailer's weight. In your case that'd be a max of 750lbs leaving 738lbs for people, gear and fuel.

If you're wondering if you're loaded properly you can weigh at a truckstop. Get the CAT Scale's "Weigh my truck" app so you can pay for the weigh and see the results on your phone. It'll tell you the total weight and the weight at each axle. It can be intimidating to weigh, but follow the instructions in the app and you'll do fine.

 

I’ve had as much as 6800 lbs behind my ‘03, without trailer brakes. Not very far… only about 15 miles… not recommended.

Towed around 5600 with it with trailer brakes. Much safer experience, but as other have mentioned… slow. I was on 33s by that point, so that didn’t help matters.

Towing with a D2 is definitely possible. I found that transmission cooling left a bit to be desired and I ended up installing a second tranny cooler which helped considerably.

in truth, towing with the D2 would be last ditch for me at this point. If it was LS swapped, no sweat. The Rover v8 is just a bit gutless for towing. It’ll do it, but itll take its time and it’ll work at it. At that weight, some kind of air bag assist would be highly recommended for long distances.

That load distribution hitch can be a blessing and a curse. You can also set it up too tight and introduce extra sway. I’ve pulled campers that it helps, and I’ve pulled campers that tow far better without.

If the d2 is the best means of towing you have at your disposal than I wouldn’t hesitate, but just be prepared to take a lot of extra time and make sure your cooling system is up to spec. In line thermostat and get an aftermarket temperature gauge in there.