This is just me, but, if someone told me they were allergic to my bird or plain didn't like it, I would try my best to be understanding, compassionate, and compromising. It's wonderful that you are taking the initiative to want to discuss it with her softly.
Explain to her what the doctor told you and maybe suggest instead of going to her house she can come over to yours or you could visit with her at a nearby restaurant.
Obviously, she loves her little guy and is defending it but that shouldn't mean friction between the two of you. Hope you work it out.