Yes they make their own trailers (box trailers, car transporters, boat trailers etc).
You'd be fine with a small trailer imo, ....as long as the towing vehicle is significantly heavier than the trailer/item you want to tow then usually it's fine. You'd need to wire it up with electrics & a number plate to keep it legit but that's fairly simple.
I never had to research fitting or getting a towbar for a 350Z before though and tbh as I said I'm not even sure if there would be any kits available in the UK for them.
If you give an Indespension branch a call though they'd be able to tell you over the phone (as we used to have books with thousands of vehicles listed with different tow bars from various tow bar manufacturers). They could even give you a quote for fitting too or you could just buy the kit yourself if they sell one & fit it yourself.
Link: http://www.indespension.co.uk/