Febreeze maybe.....
Let me jump in quickly to say never, never, never use Fabreeze on a quilt, especially if it is a gift. A lot of people are highly allergic to this stuff. Plus, it is a chemical you are spraying on your quilt and no one knows yet what the long term damage to the quilt would be with this stuff. If it stinks enough to need Fabreeze, then it needs to be cleaned.
I would recommend putting it in the wash. There really is no other way to get rid of the pet dander. I would also double rinse it, just to be sure. Since your friend is allergic to a lot of things (I completely understand!), she would not want to take it to a laundrymat since she wouldn't know what types of residue might be left in the machines there. For the dryer, my recommendation is to use the lowest setting possible; either air dry or the lowest heat setting. This will help keep the quilt from fading. If she is worried about the quilt fading, have her use a special soap made specifically for quilts. A lot of the commercial laundry soaps out there contain a chemical that fades fabrics. Hope this helps.