Back when Katrina hit, it was no more than a month that jobs came up in the construction industry to begin the rebuild. I actually applied for one of them myself but when I learned that part of the so called "cleanup construction" would mean that you might move a two-by-four and find the arm of a dead child lying underneath in the mud, I opted out.
At any rate, that is pretty much settled now. Carpenters, etc were on their way almost immediately and all the contracts are probably filled, but I would suggest a search for "Carpentry" in the New Orleans area for any that may be left.
Also, contact FEMA who handles the management of such things as natural disasters and directs the appropriate contractors to the job. These FEMA contracts are awarded long before a disaster strikes. You might get some business on the next catastrophe.