It's particularly important to not use things like colored paper and plastic bags with color/ink when initially wrapping the doll. They can be even more prone to staining than ponies!
If I ship a doll loose, I prefer to use a box (although I have shipped out a LPS Blythe in just a bubble mailer), and make sure to wrap it in acid free paper, or print-free paper towels. I also take any accessories that may come loose and seal them in a zippy bag, so they don't get lost.