So the very fact that you are asking the question may indicate you do not have the motivation or confidence.
I disagree with this statement, quite strongly. I was told that many times while I tried to figure out the course of my life, and thank god I never listened. Lack of doubt is not a predetermining factor for artistist ability or eventual success.
There is a myth that artists are born, not made. That they are fueled by some mysterious inner fire (which if you have to ask about, you can't afford). Yet I think this myth is a bunch of hooey. A lot of it is actually from marketing, for most of the 20th century's great artists were in fact amazing marketers (Picasso, Adams, Steiglitz/O'Keefe, etc.). Yes, some artists are born, but many others are made. Some artists look like artists (wear black, live in the Village, hold 3 day jobs to buy paint), and others don't (live in suburbia, have a studio in the garage next to the SUV, and wear Gap). Avoid the stereotypes, and just try to figure out your own path.
Now to your questions. Would you turn a hobby to a profession? I have. I think Hank describes the situation well. Be prepared to loose a hobby. But you may just gain a wonderful new career.
How would I go about it? First, don't fret about equipment. Make sure you have what you need to succeed, but don't blow your safety net on gadgets. That said, don't be afraid to spend money on the consumables of this art: film, ink cartridges, paper, etc. It took me months and months to get over my fear of wasting paper and ink, and realize that I needed to print if I was going to get better.
Then, scope out some time (a year, or two), and focus on jumpstarting your photographic brain. Don't try to show it, or get in galleries, or sell it to publishers during that time -- just get comfortable with the camera, your eye, and your style. You want to learn how you work: when your peak times of the day are, how long you can work before burning out, how much down time you need between projects. This was a big lesson for me. When I first started, I couldn't get going for 6 months... everything I did I hated, and I just procrastinated. But then, suddenly, it all clicked and I worked like crazy for the next 6 months. I've now learned that this is my pattern, so I don't fret if I find myself not shooting for a day, a week, a month -- I learned that it'll come back.
Hope this helps a little.