Chances are, if you have a mounted deer head, then it is a trophy buck of some size. You'll need a shipping crate large enough to accommodate the head and mount, with ample room for packing material to hold the trophy in place during shipment. Office supply stores, Mailboxes Etc., and photocopy centers stock shipping supplies. While a cardboard shipping box is adequate, depending on the value of your trophy, you might opt for a costlier wooden shipping crate. The price could buy peace of mind. You'll also want thick sheets of bubble wrap, a roll of heavy brown wrapping paper, Styrofoam popcorn and heavy packing tape.
Wherever your deer head is destined, you don't want it shifting around in the shipping crate. And you certainly don't want any petroleum-based packing materials, such as Styrofoam popcorn, melting into the fur or sticking to the antlers. Prevent this by wrapping the entire head, antlers and wall mount in heavy brown wrapping paper. Use as many layers of paper as necessary to cover the trophy and prevent the antlers from stabbing through. Secure the wrapping in several places with packing tape, then wrap the wrapping paper and trophy with several layers of bubble wrap. Secure the wrap with tape. You are shipping a fragile trophy, so plenty of padding is needed. Pour Styrofoam popcorn into your shipping crate to a depth of at least 3 inches. Add a layer of brown wrapping paper to the Styrofoam packing material, then carefully place your wrapped deer head and mount inside the crate. Secure it with wads of wrapping paper to prevent the trophy from shifting around, then fill in all the gaps and crevices with Styrofoam popcorn.
If you've ever seen one of those before and after images of a box entering and leaving the post office, you'll want to put extra packing tape over the crate flaps and reinforce the corners, as well.
Pay first-class shipping at the post office or shipping center. You're not mailing a T-shirt to your cousin; this is a prized trophy that needs the best treatment. You'll probably want to insure the package, especially if you've seen the cost of taxidermy services lately. The mounting and preserving service is expensive enough, but the trophy itself may be priceless.