I did a similar trip with a friend. He shipped his GT3 to Germany for the summer. I just went for 10 days with him and rented a new Porsche from Avis for myself. It was an amazing trip!
I don't remember the exact shipping costs, but they were more then I expected. For just a month i think it might still be cheaper to rent when considering all costs. When i went 2 years ago it cost my ~180 euros per day for a new 911 or panamera. If shipping your own car, it has to be owned out right. If you are interested in more details let me low and i will get them from my friend.