That's unprofessional to the point of extortion in my book. If she gets a full commission from you, her responsibility would be to you, the seller, not her friend, the buyer. In your shoes, I would politely tell the agent the property is for sale by owner, and if she wants a commission, she needs to speak to the prospect. If she gets pushy, complain to her broker.
However, it's not uncommon for a FSBO seller to offer half of the typical commission rate as an incentive for a sale. That's all they would get anyway if both parties were represented. I would think about that in future negotiations.