Does anyone know how to professionally ship cupcakes?!

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In order to ensure that perishable food items delivered through the mail do not spoil, it is imperative to understand and abide by standard regulations set by the United States Department of Transportation (DOT) and the International Air Transport Association (IATA). A perishable item will go bad after a period of time if it is exposed to extreme temperatures or high humidity, so it is important to securely package the product in a very cold environment to be delivered next day mail.

Pack the item in a box sturdy enough to withstand handling at various orientations.

Use a box with 1-1/2" thick insulated walls such as an expandable foam box, to keep high temperatures from penetrating the container.

Place dry ice or gel coolants all around the product in the foam box to keep the items refrigerated. Dry ice should be used for any item that must remain frozen; however, there are safety concerns involved when packaging dry ice. If using gel coolants, follow the recommendations of the manufacturer before placing in your package. Keep in mind that refrigerated goods must be kept at a temperature between 32 F and 60 F.

Place the foam box in a shipping container and pack with bubble wrap to keep the items secure.

Secure the box with weatherproof and pressure sensitive tape on all flaps and seams.

Fill out a shipping label and place it on the upright side of the box. Using a permanent marker, label it "perishable" or "keep refrigerated." If using dry ice, you will be required to place a dry ice label on the largest area of the box.

However considering that it is a perishable object, and you do want to ship it as fresh as possible you might not need to refrigerate or pack in dry ice and all that jazz. But you might consider it courtesy to do so.
Considering all this as well. as long as you mark the box "Perishable" It should be good.
Listed bellow in sources are a few other tips and advice for you to consider.
Good luck buddy.

http://www.ehow.com/how_6904312_ship-perishable-foods.html

http://cpa.utk.edu/pdffiles/cpa81.pdf

http://homecooking.about.com/od/holidayandpartyrecipes/a/foodmailtips.htm