Usually when you show up to pickup a trailer or dolly they will want to make sure that the tow rig will handle both the trailer and the vehicle being loaded on it. At least that has been the case when I have rented a trailer.
You didn't say how far you have to go to get the truck but usually it is less expensive to rent the trailer where you live and tow it to where the truck is. Unless you figure that the gas savings of running without the trailer will be more than the one way rental.
Also note any dings or damage to the trailer when you pick it up. I'd go so far as to take photos of any damage when I picked the trailer up and let the rental agent know that you want the damage noted in the paper work. That will save you any hassles later.
Also make sure that you take along tiedowns or rope to tie any loose pieces that may be in the bed such as fenders, hood or what not. You don't want anything flying out of or off of the truck when you tow it down the highway.
And lastly, unless the truck runs and you can drive it on the trailer take along a good come along or something else to winch the truck up on the trailer. I have used my small chain hoist to pull several rigs on trailers and tow dollys and it works well.
