The fact that your dad owns the trailer won't eliminate DOT concerns. You will own the truck and be the driver. DOT could (probably accurately) interpret that as hauling for hire with your dad as shipper.
Who owns the trailer and the cars in the trailer and why will you be transporting them is the question DOT will ask and want proof of.
Is your dad in the used car business? If you use his trailer to pick up or deliver cars bought or sold as part of his business you are commercial and subject to DOT rules.
Even if you buy or own the cars but they are not registered to you for personal use you are commercial.
If you borrow your dad's trailer and you own classic cars and haul them to car shows only for private display and then return them home that would be private and not subject to DOT. If your dad owns the classis cars but is riding with you that could be explained as you are going to the shows together. If your dad owns the cars but is not present you are commercial because you are hauling for him, even if he doesn't sell them. If you sell the cars at shows that is commercial. DOT rules are basic and straightforward. Commercial activity is subject to DOT rules. DOT rules are only made complex by the hundreds of ways the rest of us try to game the system to get around the obvious: all commercial transportation activity is subject to DOT rules.
With a big gooseneck trailer like that a DOT officer is likely to assume commercial purpose and check you. Any DOT officer knows your little SRW truck has a rear GAWR of about 6500# max and will know that a loaded gooseneck of that size has a hitch weight of at least 4500 #. Duhhh. Is he going to stop you? Yes.
My son-in-law is a very successful general contractor who builds and remodels commercial buildings. He purchased one fifth wheel travel trailer from me and had me locate and buy another for him. Both trailers are used as temporary housing for his job superintendents on remote worksites. My sil pays me to move and set them up when jobs start and end. That is commercial. I skirt the rules and don't comply with DOT because the trailers are not shiny new and they both display TX plates. I look like an ordinary RVer when I'm pulling them. But if I ever get stopped and looked at by a DOT LEO I'm not the registered owner of the trailer and could be subject to fines.
Even worse, my sil has a Corvette collection and a fancy enclosed car hauler trailer with his name and a big, bold, colorful logo painted on the trailer sides. I'm the "go-fer" when he buys them. I've pulled his trailer to NC, TN, KS, and OK picking up Corvettes he bought on eBay. I pretend to own the trailer and the Corvette inside on the backhaul and run the scales but if I'm ever pulled in and asked for registration I'm in trouble. I could lie to the DOT officer and claim I'm just doing it as a favor for my sil but real DOT cops aren't stupid (some ordinary LEO are) and I hope they don't think I look stupid enough to use my truck to pull my sil's trailer several thousand miles just because he's a good guy. Obviously I am compensated for my efforts and use of my truck.
I hated pulling the big Weekend Warriers because they were too heavy, too long, too tall, too hard on my truck, and required too much effort and attention on my part. Negotiating heavy LA freeway traffic or small city streets on the delivery end required very close attention to avoid getting into trouble. The tail end of those things seemed like it was a block behind me. Try backing one from a narrow city street into a narrow driveway on your blindside with oncoming traffic and traffic stopped impatiently behind you without a helper to help guide you or help with traffic control. Trailers that large overwhelm an ordinary little dually not to mention a SRW 2500 or 3500. Just towing them caused me to feel the stress being placed on the truck and worry about the possible consequences of a blown tire or failed seven pin connector (surprise, no brakes!) Simply not fun.
My own personal HH fifth wheel has a GVWR of 14,100# and weighs 14k# for vacation travel. My truck and the trailer are impeccable maintained using nothing but top quality Michelin tires. I would not want to own and pull a trailer that weighed even 14,500#. Sure, my ISB6. 7/Aisin cab and chassis can pull more but Dodge engineers are not stupid people. Their GCWR calculations make a lot of sense. IMO any trailer that creates a GCWR of one pound over Dodge's GCWR for that particular truck and drivetrain is in MDT territory.
Some will read this and think "Harvey's a sissy" or "... . an old man. " You are entitled to your opinion. I've done it for many thousands of miles and know what it's like. When I was transporting for a company in Fontana, CA I was dispatched to pick up a new Travel Supreme at a now defunct dealer over across greater LA in one of the coastal cities. I was to deliver it to the new owner in a high dollar restricted luxury RV park way out in Palm Desert. I drove all the way through LA traffic to the dealer and picked up the trailer. When I rolled away and tested the brakes I had NO brakes! . . . on a 20,000 lb. 45' Travel Supreme just purchased for about $150,000. I stopped and checked my seven pin receptacle and the trailer's harness. Both were fine. It was mid afternoon and I knew that dealer wouldn't be able to repair it that day and if I asked my haul would be terminated. So I made the obviously extremely risky decision to pull it w/o brakes. It was going to be set up permanently and never moved again anyway. I pulled that miserable monster approximately 180 miles across Los Angeles in afternoon traffic with no brakes whatsoever and set it up unscathed for the doctor and his wife in the luxury resort RV park. That trailer required a MDT IH 4400 or FL60, even with trailer brakes working.
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