You might want to check your states laws on that one. You also need to check the state laws of every state you are traveling through. For instance, if you are traveling through NY, don't bother. Just buy a new gun in Alaska.
This might help some NRA-ILA ::
Also, I'm not sure that you can carry ammo at all. I'm fairly certain taht the pistol in a hardside case, declaired and locked in the bag will be fine, but you should call your airline first. They will be the final deciders as to wether you are allowed to board with your firearm at all.