Qualifications
As with any art, you don't really need a fancy degree to do it. The basic qualifications come from inside you. We're talking about creativity and imagination here. And practice, which is important too; the only way to "find" yourself as an artist is to continue making art. This is also a great way to find out if you hate it―repetition will either make you great, or make you go insane (or if you're a van Gogh type, maybe a little of both).
You'll need a lot of patience, too, especially if you're trying to make money at this career. Remember: just because you made something, it doesn't mean the local art gallery wants it, no matter how many fancy degrees you have.
Also, as with any art, if you want to sell out and make a lot of money doing it, you actually might need a fancy degree. One of the best paying industries for sculptors is the movie industry. From art direction to setting to special effects, movies need talented artists to imagine and create incredible works of art on a deadline and (ideally) on budget.
Studios typically want to keep all those people in-house too, so they're not just looking for awesome sculptors, they're looking for the right kind of awesome sculptors. They'll want to see that bachelor's degree, plus those references, that mentorship, and all the incredible works of art you've been designing since you first rolled Play-Doh into a tube snake. That big-time opportunity is out there, but you have to really want it first.