For what it's worth I've got a dealer tow package on a Canadian truck which means it's got 4 pin wiring and the class IV hitch (dealer tow) and the big battery and alternator (CDN). I just did a 4 to 7 pin conversion, cost was about $120 from etrailer.com. Yes you could do it cheaper but I went with a good quality 4 and 7 pin connector (no stupid adapters to lose), the matching pigtail harness and a breaker box to install up to 7 breakers for trailer wiring and then lights, compressor, etc that I can add in the future. A good proportional brake controller is about that too and you need and definitely want a brake controller on any reasonably heavy trailer with these trucks.
In the future I plan to do a trans temp gauge and trans cooler, I'm not doing an engine oil cooler. I don't think it's necessary in a cooler climate.
Back to your plans though, I'd have to say I think you need more truck... The enclosed 6x14 tandem axle I pull rated for 7k lbs weighs 1700 empty. Just looked up some car haulers and an open deck weighs around 2000 lbs, enclosed car haulers look to start around 3000 lbs. If your car weighs in at 4300lbs... You're either 'just' under the upper end of the weight limit or well over and you haven't even considered other stuff you might be taking. Having towed and hauled in my V6 DC with larger loads I'd stay away from a trailer that heavy, it's not what you want to hear but it's just not enough truck.