David,
Welcome to JavaRanch. I hope you enjoy using Java and I hope you enjoy it here. I stumbled upon this site a couple years ago when I was looking to get my certification. Obviously, I've never left.
I'd have a hard time giving you a set timeline based on the fact that Java is your first programming language. People learn at different rates and if I say it will take you 1 month to prepare, it might actually take you 2 weeks or it might take you 3 months. I do have a suggestion, though...
Start my going to
Dan Chisholm's Web Site. He has some excellent mock exams there. Try taking some of the mock exams there - don't take them all, just sample about 20-30 questions from the various topics and see how you make out. This should give you a decent baseline of where you are today. That may help you decide how long it will take for you to prepare. Don't sweat it if you don't score well - there's a bit of an art to taking the SCJP exam that you'll become aware of once you start taking more mock exams.
Once you know where you sit, get yourself a book. It wasn't around when I was getting certified, but I've heard
K&B is very good (and, yes, that stands for Kathy and Bert, as in Kathy Sierra and Bert Bates). Do your studying and start getting yourself prepared.
Be sure to stop in here often and check out the resources at the top of this forum and around the ranch (there's a lot more here than the forums, believe it or not). Best of luck to ya, pard'ner.