Qualifications
Careers in the shipwrighting industry can vary from low-level, hammer-in-rivets type of work to high-level, manage-brainy-engineers type of work. Whatever it is that you're doing, though, it's going to require you to walk the same basic road toward professionally designing and engineering watercraft.
Like most things that pay more than $30,000 a year, being a shipwright means getting a bachelor's degree. Specifically, you're going to want to look for something in marine engineering or naval architecture. These can be harder to come by than, say, philosophy programs, so you might need to focus your college search on the coasts (a little secret: that's where the ships live).
Succeeding in that sort of work is going to take a special sort of person: one who's tech-savvy, math-savvy, creative, and not hydrophobic. Depending on the specific career path you want to follow, you may be required (or incentivized) to track down certain licenses and certifications. These are far too numerous and varied for us to list out here, but a common example would be a mariner's license.
Your best bet to make it as a shipwright is to get your education going, then start to research exactly what you need for whatever aspect of ship creation strikes your fancy.