Would be best to talk to the NE DMV. Every state is a little bit different. If the truck looks stock, DON'T tell them it is going to be used for competition w/ a purse. Will be considered commercial. A lot more hassle. Unless it has changed (or the cop was just an a-hole) in IA, the trailer needs to be licensed for the 24k. I know a guy that had the truck licensed for all of it, and they still gave him a fine in Des Moines, Ia. Plate was on the trailer, too. IIRC, he was from NE as well. I would license the truck fror 12k.
If the commercial pickup trucks go across the scales, I've never seen it around here. I drive a big truck, so I have to. Never have with the Ram. Most of my towing is on back roads with ag equipment (ie, low speed)