First put your (dry, room temp) quilt in the dryer on * AIR only * for about 20 minutes. This will help get some of the dander off the quilt (especially if you have cats or dogs that share your quilt).
Then shake your quilt outside to remove any remaining loose dander. Place your quilt in clean freshly fallen snow. Let it lay in the snow for about 15 minutes. Shake the snow off the quilt, turn it over and place it in the another clean area of snow for 15 minutes and then shake the quilt. If it's a sunny day, hang it out to freshen.