NO. Don't do that. There's a lot of GC scams going around, and many involve getting the info up front then filing for a SNAD claiming the card arrived with no $ value on it. Sure, you'll have the fBay email showing that you gave her the info, but that does not guarantee you would win the claim. Plus, if she mails it back and shows proof of delivery, PayFoe might refund her money because you got the item back. And like someone said, how do you know for sure your giving the info to the person who actually paid for the card and not someone else in that household? And, what if it turns out to be an unauthorized transaction--which is sooo in vogue right now? As far as I know, unless you mail that card, you're not covered by seller's protection, as you must show proof of shipment and delivery to qualify.
Selling GC on fBay is super risky these days.