I don't think you'll have trouble with the truck itself. If it's diesel, make sure you don't go to the wrong pump. These trucks aren't always that well maintained and they don't stop quickly even when they are, so definitely don't tailgate. Ask them to double-check the tire pressures in front of you when you pick it up. Running that far on underinflated tires would be unsafe and would add to your fuel cost.
As for the trailer, do you know the technique for turning while backing up? If not, you'll need to read up on that and practice in an empty parking lot. Your friend should get out and help to direct you. You probably want to avoid situations where you have to back up in the first place.
These trucks sometimes leak in heavy rain. You might want to cover certain items with plastic dropcloths or keep them off the floor.
If you happen to be coming from central New York, I'd suggest looping around Washington on I-81, I-66, and US 17. The Beltway wouldn't be fun. Definitely take the bypasses around Richmond and Jacksonville.
If you don't have a GPS system with points of interest, consider buying the book "I-95 Exit Information Guide" at http://www.i95exitguide.com.
As for gas prices, South Carolina will be the cheapest, so fill up there if you can. Also, Georgia will probably be a little cheaper than Florida if my past experience holds.
It'll be a bit of an adventure, but you'll have fun.