This is going to cost just a little bit, but it may be worth it.
Check the doll and her things for mildew spots. If anything is mildewed, you are not going to salvage much. You will need a professional restorer for mildew damage.
Now:
Put fresh kitty litter into a large plastic container - large enough to hole the doll and all her stinky accessories.
Lay a sheet of lightweight fabric or white tissue sheets (gift wrap tissue) over the litter. lay out the doll and her things on top. Close the lid and leave it to absorb the odors for at least a week.
Check after a week and give everything the deep sniff smell. Get it right up to your nose and sniff deeply. If it smells good, leave it one more week just to be sure. Then air out in a protected shaded spot (a covered porch is good) on a sunny day for at least 24 hours. If it still smells good, package it as though you were going to ship, wait one more week and then open and smell. If all is good - ship the doll.
All these checks are to be certain the musty smell is gone.
If you want, you can alternate kitty litter with fresh coffee grounds (un-brewed - straight from the can. use a couple of pounds of ground coffee under the doll (use several sheets of tissue or fabric to protect the doll from coffee oils).
When you are done, you can use the coffee in your compost (don't think it's good to brew after absorbing odors)
If the doll is not expensive or valuable, you might very lightly mist the fabrics with Febreeze, but that's sometimes chancy with some fabrics. You might want to mist some packing tissue with febreeze and lay in the box, separated from the doll with more tissue to reduce transit odors.
