I have to admit I wouldn't drive 12 hours unless the eggs were very, very special.
I've shipped eggs thousands of miles and never had one break. I've bought bubble wrap (the little bubble ones) and then wrap each egg individually. Then I fill a med or large flat rate priority box with packing peanuts. If I can, I'll stick the wrapped eggs in an egg carton and tape it shut, and then stick into the box of packing peanuts, making sure there's peanuts on all sides and fairly full so that it can't wiggle much. Tape it all up, and write fragile all over it. I've had good luck with it. Unfortunately, my buyer reported that all eggs made it just fine, but never told me the hatch rate.
I've received eggs shipped the same way, had an 80% hatch rate, which is awesome, considering they were shipped 2000 miles during the second week of December.
Oh, and it's a good idea to ship on a Monday so that the eggs will definitely reach their destination by Saturday.