Paul, I have shipped a lot of carvings and never had one arrive broken or damaged in any way.
First, yes, absolutely, you want to insure it! My experience is only dealing with UPS, as far as shipping carvings. It was suggested to me as the best method and I've just stuck with them.
I wrap my carving in bubble wrap, as Garry mentioned, using masking tape to secure the bubble wrap in place. I place this in a box about an inch or so larger than the bubble wrapped carving. I usually wad up plastic grocery bags for the padding around the piece in this box....works as well as peanuts and it's free padding!
Next I pack that box into another box that is about two inches larger all the way around. Double boxing is the very safest way to send anything! Again I use wadded up plastic bags to pack around this box. (Everyone saves me their plastic bags, they love getting rid of them and I love having them!)
Before you seal the box, it's a very good idea to put a note in the box that has both your name, address and phone number on it and the name, address and phone number of where it's going to. Tape the box up securely and ship it.
I believe UPS covers all their parcels for $100.00 value automatically, you have to purchase additional insurance if it's necessary. Check to see, whatever method of shipping you use, you definitely want your piece insured for the full value!
Hope this helps! Now how about showing us a picture before you ship it!

Deborah