I've shipped large iced layer cakes across the country several times. I start with an inexpensive plastic "cake safe" from the dollar store ($8-$12). I put a dollop of icing on the base to anchor the cake in place. I assemble the cake, ice it, and let the icing harden a bit (best to use the sort of icing which firms up, not a fluffy egg-white frosting). I cover the cake all over with plastic wrap (because the icing is firm, right? so it won't stick) and then put a layer of clean small-bubble bubble wrap between the cake and the dome lid, filling all the space so the cake can't shift. (This takes trial and error and reorganizing the placement of the bubble wrap.) I use mylar packing tape to secure the lid firmly so it can't come off. Then the cake safe is put in a large box, surrounded on all sides by newspaper or other packing material, again, placed so that it doesn't shift around. I've usually sent it UPS -- they seem to be a little bit better on not throwing it around if it's marked "FRAGILE". It's not cheap -- depending on the weight, $35-$50 just for shipping -- but if you've got a child who won't be home for their birthday, it's a cheap way to make her happy.
The trick, as others here have noted, is to make sure that nothing, but NOTHING, can shift during shipping. Well-wrapped, and delivered in two or three days, the cake will still be fresh and tasty.
October 19, 2014 at 10:40pm