It is probably perfectly acceptable in many areas to package eggs in a box, gently rolled in one layer of bubble wrap, and marked "fragile" in tiny letters near the shipping label.
On the other hand, long distances and shipping to Alaska calls for something different entirely.
Packages shipping to Alaska require switching planes several times as well as trips through even more sort facilities. Because of this, many packages are handled more roughly and in a surprising number of cases, handled by an automated, electronic mechanism that cannot distinguish between a living, fragile creature in a box or a durable box of nothing but books. For this reason, one shipping eggs to Alaska (or any distance, when it can be afforded) should take not one but ALL necessary precautions for egg shipping.
The first box I have ever received that contained all intact eggs was from Corancher. Excuse the cell phone pictures, please.
This first picture shows how she wrapped each individual egg. Each was wrapped in damp paper towel, and then placed in the common taped-end bubble wrap pocket, then rolled up. The eggs were very cool when they arrived, and did not appear to be overly jostled.
The eggs were placed on a bed of shredded paper, and fitted into a small box. They were not crammed in, but fitted well enough that they would not jostle around or shift in transit. The bed of shredded paper is IMPORTANT. Any time a box receives pressure from the outside, there needs to be space between the eggs and the walls of the box. Without this cushion, any pressure on the outer edge becomes pressure on the eggs. This has led to many broken eggs on my end.
One of the MOST important steps is packaging the small box inside of a larger box. Again, any pressure put on the outside of the box will transfer directly and since packages shipping to Alaska endure excessive *trauma* (yep...I used the word trauma!) every little but of extra precaution is great. This box was padded into another box, which is ideal. If this box is against the side of the outer box, the pressure will transfer directly through.
Finally, writing "Fragile" in large red letters on EVERY SIDE is worth the extra effort in hopes that the package will be handled more carefully. This is not always the case, however. The absolute best bet is attaching a label that informs the handlers that there are LIVE ANIMALS inside. Most people, even if they are careless with a "fragile" parcel, will take extra care if they know there is life inside. One of the most gently handled boxes I got had a large red paper on the front that said "live critters."
Even the best packaged eggs are at risk for damage because the Alaska shipping process is very rough and not well maintained. It's best to set your package for the best chance at success!