There's a good chance you could be ready in 6 months. There are some variables, though, like how fit you were before you started riding, for one. A big factor is how much climbing there is in the century. That makes a huge difference. If it's relatively flat, I'd say you are probably fine. Elevation gain and temperature make a big difference as well.

What I would do is see how your training progresses, how you feel on the bike as you ride longer and longer distances. When you ride your first century, you'll likely be on the bike for 6+ hours, not including breaks, (which help a lot, by the way). I did my first century on a tandem, so I had the help of my strong husband. Almost a year later, after continuous riding, I was training for my first century on a single. I was building up with longer rides each week and when I was nearing the end of my 65 mile ride a couple of weeks before the century, I was miserable. I was just so uncomfortable on the bike, I couldn't imagine riding a full hundred miles. And there was some considerable climbing ... 3500-4000 feet (it's hard to find anything flat in So. Cal.). I opted to ride the half century instead and was very happy I did. I think it was 60 or 65 miles, actually. But either way, it was a much more pleasant riding experience and it gave me more training for the century I DID do just a few weeks later. (And a professional bike fit helped a ton as well.) So listen to your body. And if the event you are doing offers shorter distances, be prepared to change you plan if you aren't quite up for it.

When you are training for longer distances, you don't have to make every ride a long distance ride, by the way. Make one of your rides each week longer and longer until you hit around 70 miles a week or two before the century. The in between rides should be shorter, but they are important to help you develop a base.

One of the things that helps me get through centuries is the SAG stops (aid stations). You should get a route slip at the beginning of the ride. Make a note of when the first SAG is, usually around 15-20 miles, and all you have to do is focus on that first 15-20 miles. Before you get back on the bike, make a note of when the next SAG is. If it's at mile 38, just focus on getting to mile 38.

Have fun with your new bike ... and doing your first event on it.