Wallace Hardy makes a good point about the Mississippi between Baton Rouge and New Orleans (and down to Venice)--and this is the only part I have personally boated on in trawlers from 32 to 42 feet.
The Port Alan option takes the boater down the Atchafalaya River to Morgan City, where one joins the Gulf Coast ICW. The current in the Atchafalaya can be more than in the Mississippi because of the steeper drop per mile, in the shorter route. The overall trip will be slightly longer because of the ICW travel. There is little in the way of fuel (except if you can get some one at a ramp to take you to a gas station--which is likely). But there are good anchorages, and a real taste of LA.
There are a number of Kayaks and canoes who have done the river--and their experience might be better for the lower river than the link Jim gave you (Where the open boat took the Ten Tombigbee waterway, instead of the lower river to Mobile)
See:
http://www.barbarakeithdesigns.com/mississippi.htm
http://www.mississippiriverresource.com/
http://www.bucktrack.com/Canoeing_Down_the_Mississippi.html
Be sure and check the Army corp of engineers web sites for hazards, current, stage and lock conditions:
http://www.mvd.usace.army.mil/
A number of larger long range vessels which have done the full river, and some before the Tombigbee waterway (which really opened up the Great loop).
In 1979 a 16 foot aluminum skiff was vehicle for author of the book
"Old Glory, a voyage down the Mississippi River, by Jonathan Raban . (also available by Kindle)
One piece of equipment I would seriously consider, which might seem overkill for a 16 foot C Dory, is a radio receiver which also receives AIS signals. This will allow you to easily identify near by river tugs and commercial vessels for safety and navigational communication. Standard Horizon MATRIX AIS GX2100B --this is the older model, often still in stock for less than $300, including a 30 watt loud hailer/fog horn.
