When I was a senior in college, I started applying for jobs in January- right at the beginning of the semester. I had my job secured by March. This was 6 years ago though before the economy tanked and there were more jobs for new grads. In that year alone, my floor hired NINE new grads staggered from July-the following March. Things definitely changed as the economy did though... in 2008, we hired 3 new grads, in 2009 none, in 2010 none and in 2011-2012 the hospital instituted a "new grad only" policy for new nursing hires because they're cheaper. The floor I used to work on has hired 5 in the past year... that's to replace the 14 or so people who've left in that same year.
Check with the hospitals in your area or the ones around the country you are looking to apply to (If I hadn't been hired at the pediatric hospital I'd done clinicals at, I was going to apply to other pediatric hospitals around the country... I knew I had NO desire to be an adult nurse) and see when they start accepting new grad applications. Good luck!
It may vary by hospital but when I was a new grad in 2009 I applied in December of 2008, interviewed & was hired in January 2009, graduated in May and started my job in August. So for an August start date I had applied 9 months prior.