It's up to the dealership, but I highly doubt it. alot of dealerships will not let you test drive a GT right now, reguardless of age, because they don't want the miles put on them. When I bought my '03, they wouldn't let me drive a GT. They'd let me drive a v6, but not a GT, and I was 22. It's up to the dealer, but it'd highly unlikely to find a dealer who will let you drive such a car.
As for being too young, most of me says that is too young to have a car so powerful, and such a nice car. Most people's first cars are >$1000 junkers. Not always because they don't have money, but you're 5x more likely to get in a wreck in your first two years of driving, than after. Whether it's a beater, or a 300HP sports car. Get the GT, but have a beater, and only drive the GT on days when it's not raining, and won't be heavy traffic. That'd be the smart thing to do. The other part of me, though, says I wish I had a GT for my first car, and I, too, had a muscle car as a first car, and never so much as dinged it. It also was a beater, that only cost $500. So there ya' go.