Welcome to the forum, and congrats on your new purchase (a very nice RV indeed) and also congrats on asking the most hotly debated question on all forums with this type.
I looked at three 362RD's on line and they averaged about 2700 pounds of pin weight. Your 2500 probably has a cargo capacity of about 22-2400 pounds. Take your 2700 pounds and add what Chip mentioned:
5v'er hitch, 200 lbs,
you, wife, kids, dog, 700 lbs,
diesel fuel and miscellaneous luggage 300 lbs
Realize now that I'm just speculating but you have entered the maximum of most SRW one tons and probably into the dually range. With careful configuration (storing the dog and wife for instance in the back of the trailer
) and you'll do okay with most high range SRW 350/3500's.
I'm not berating you for your choice. You asked and we answered. There are many on this site who haul way overloaded, most do not.
Nonetheless, welcome to the forum. We're glad you're here.