Look on the end of the drivers door or on the drivers door post, on the sticker there it will have a GVW weight, that is the weight rating of the truck.  If your truck weighs 25000 empty, the gvw will be over 26000.  Usually a dual wheel gooseneck and a 3/4 ton pickup has a GVW over 26000.  The trailer you are getting will have a GVW of 50-60000lbs

You can get a trip permit for the day, licensing the truck for less than 26000 won't make any difference.   But you would still need the medical card to go out of state.  You could take your truck, licensed at 80000 or whatever weight for your state, go around the weigh scales and if you get stopped pay the fine.  

Or hire a trucker to go get your trailer.