We always take a dozen fresh eggs on every trip.  We take them in the original carton, put that inside a jumbo zip-lock bag, put it in a paper grocery bag, fold that down and duct-tape it under the stern seat of the canoe.  Keeps it out of the sun and keeps it from being bumped around.  Nothing larger than a "large" egg, mediums would be stronger if you can find them.  Get ones with the freshest possible date.  We just buy them from the grocery store once we are in Ely or Grand Marais.

If the Davidson's Pasteurized eggs were available in our area (our daughter can get them in the Chicago area) we would definitely take those, as I think they would be much safer, but we cannot find them in Michigan or in Minnesota so far.

In camp we are careful to keep the egg bag out of the sun.  If the temperatures run very hot for several days, we will use up the egg supply by the fifth day or so.  We don't go in July or August, so extreme heat usually isn't a problem.  And there are just two of us, so a dozen is enough, but you could easily use this method with two dozen also.

Like others, I have tried the plastic containers made for camping with eggs, and had broken eggs all over everything!  Never again!!