Definitely put it into some type of waterproof cover. I save all my zipper plastic bags that my sheets come in. Also include a name and address inside with the quilt, in case the box gets water damage.
I have use UPS and USPS and none of them are fail proof. Notify the sender so they can be on the look out for a package. Dogs within reach of packages can be just as bad as a rainy day. Also with the holidays nearing there seems to be an increase of packages being removed from people's front stoop.