I don't think there is any time you have to be disabled before benefits, just as someone else said you have to be expected to be disabled for at least a year. My date of disability was Aug. 6 and I was approved in April of the following year (only 11 weeks after applying, so really fast as well). You don't get paid for 6 months from date of disability (I think, don't completely trust my memory on that) but you can apply at any time.

You can call your local social security office with questions.