If you have never dealt with dry ice, there are a few things to consider.
Don't put it near anything that could freezer burn. (EX meat) Place some cardboard between meat/food and ice.
Handle with gloves. You will get frostbite.
Use gloves when handling.
The meat that comes in contact with dry ice will rapidly get freezer burn if you don't put thick cardboard between them.
I would duct tape the seams of the cooler, to keep it as airtight as possible....that will reduce the rate at which the frozen CO2 evaporates (or whatever it does).
I have found it more and more difficult to locate dry ice over the past few years....are you certain that your source still provides it?
I had some friends that when to CO one year and packed they food up in a cooler with dry ice when they left TN. they said they liked to have starved because it took 2 days to thaw out their meat when they got there. the daytime air temps were in the 50s.
Good for keeping frozen stuff frozen for like 3 days or so. But probably not to be used to keep stuff cool.
And you must be careful about the outgassing as mentioned eddie c.
And +3 on eddies c's comment. Don't store in your rig.
We use it freeze meat for the flight home if we can't find someone with a freezer.
Honestly I don't think it would last much if any longer than just a bunch of ice would in a good cooler. A good cooler if cared for will keep thing 5-7 days easy. I'm not sure the dry ice would last that long. It will be lighter and take less space, but you're gonna freeze some things. Oh, and it's kinda pricy in comparison too.
I've heard of folks using a combo of ice and dry ice. Not sure how that worked out but the theory was the regular ice insulates the food from freezing and the dry ice helped keep the regular ice from thawing as fast. In theory.