I plan to travel to New Orleans next spring, when is the optimal time to book?

Sometimes booking early (at the earliest possible time 300+ days before travel) can be cheap, but in my expereince the rates show no real variance day by day or by time this far out.

If we wait till the last minute you can get good deals, but on the other hand prices often tend to go up.

Is there an optimal time to buy tickets?

Early not always guarantees cheaper. Next year is too far ahead, and sure you can book, but sometimes it is better to monitor the prices for some time. Last minute deals are usually more expensive than those that are offered 3-5 weeks before leaving. Farecast is good website for such information.

Here is a video that shows how and when prices drop or go up:

http://blog.lessno.com/archives/186