Question about trailer to haul truck

[72step]

I am considering entering my truck in a show about 100 miles away from home but I wanted to tow it in my trailer. My trailer is 16ft flat 83" wide but the drawback is it has rails. I don't want to screw my truck up. Is this easily doable in my trailer? The measuring tape says it will work, I just want yall's opinions/experiences. I don't want to drive it as the truck has been sitting stored for 10 years, not sure it might have some bugs to work out and I don't want to have roadside trouble in the dead of winter. Thanks...