2012 Explorer will likely have the same 5000 lbs rating as the 2011 Explorer.
Combined weight rating (GCVWR) is 10,125 lbs. Subtract the 4557 dry weight, and you are left with 5568 lbs for the loaded camper, and any people/cargo in the Explorer. Subtract the 3400 lbs empty camper, and you are left with 2168 lbs for any people/cargo in either vehicle. Keep going subtracting your known weights, and determine if you are OK.
You really should get an accurate loaded weight of the camper. Going by the unloaded/dry weight (3400) is not a great way to go, since that weight does not include any factory options (A/C, stove, etc), or dealer options (battery, LP tanks, etc), nor any of your gear/luggage.
For 1000 miles trips, I assume you will hit some decent hills. I would want some more cushion if that's the case, and not take things right to the limit.
As far as mileage, you are used to a straight-6 which was a good motor that didn't get great gas mileage IIRC. With the modern Explorer V6, you should probably expect much better gas mileage when NOT towing, and probably comparable gas mileage while towing, compared to your Jeep (or maybe worse?). But remember that towing is a small percentage of overall mileage. Maybe a little more for you, but still probably only 10%.
Get an actual weight on your trailer.