Check the owner's manual and see what it's rated to tow. Don't forget to add the weight of the trailer to the weight of the car. My guess is that it's not rated for this much, though.
If you do decide to do this, I'd at least consider putting a transmission cooler on the tow vehicle. If you overheat the trans and cook it, that could be a $2500 repair bill. It would certainly be cheaper to drive the Z, rather than pay this bill, even if you have to make some repairs and license and insure it temporarily.