If you want to go by car from New York City to New Orleans, the shortest way will take about 21 hours and 30 minutes (without sleep). The distance between those cities amounts about 1.306 miles/2.102 kilometers.

By airplane you will need about three hours to cover the distance from New York to New Orleans or reverse.

The hurricane Katrina would not need that much time. Here is a small timeline that shows a few stations of this natural disaster.

On August 23, 2005:

Katrina shaped as a tropical depression in the area of the southeastern Bahamas.

On the morning of August 24:

Katrina was upgraded to the tropical storm status. The storm moved to the direction of Florida.

On the morning of August 25:

Two hours before landfall, between Hallandale Beach and Aventura, Katrina transformed into a hurricane. The storm destabilized at land. Nevertheless it received hurricane status again only one hour after being at the Gulf of Mexico.
After nine hours the storm intensified its power and grew to a category 5 hurricane.

On Saturday, August 27:

Katrina almost doubled its size and intensified again.

On the morning of August 28:

Peak strength: 1800 UTC
Maximum sustained winds: 175 mph
Minimum central pressure: 902 mbar

On Monday, August 29:

The hurricane prepared the second landfall at 1110 UTC as a Category 3 hurricane with winds of about 125 mph near Buras-Triumph in Louisiana. The third landfall had been near the border to Louisiana and Mississippi.
After 150 miles on land Katrina lost its hurricane strength and was downgraded to a depression.