You need to think about the beer(s) you would want to enter, and how long it takes to mature them. Look to see when the entries are due, then count back on the calendar to see when to brew. You might allow an extra week or 2 for fine tuning of the carbonation in kegs, packaging, etc. if you don't have all contingencies in you original timing.
I do lagers in the late December to Jan, stronger ones first, so that they are lagered out. A German Wheat would be brewed only 2-3 weeks or so before the entry date for the first round (I don't brew these, so chime in if anyone has better timing). You might want to think about when the beer is at its best, and time back from the judging window, rather than the shipping window.
Experience with certain beer styles plays a part in this. In Brewing Better Beer Gordon Strong has a chapter on competitions and how to do it, and it has good points on the process.