We had a co-worker with a very severe peanut allergy and two with significant shell-fish allergies. A the time we also had a relatively open-concept office plan. Peanut products were banned in our office, but no one complained or struggled with it.
For those who say "Well it's up to her to bring her Epi-Pen." This is very true, however Epi-Pens are used in critical life-threatening situations and even with an emergency Epi-Pen injection, the person may still die. It's not at all like when my exBF had a cat allergy so he'd take a lot of Benedryl before we went to my cat-loving grandma's house.
In the seven years that she worked for our company, we only had one incident when a new employee hadn't been notified about brining peanut products to the office. Someone noticed the allergic employee's face looked really puffy, and she was taken to the hospital for antihistamines by IV. She did not require her Epi-Pen because she was not suffering from anaphylaxis (yet).
Overall, the peanut ban really didn't affect anyone very much. The two with shellfish allergies were fine as long as they didn't try to eat it. (And sadly one was very, very fond of shellfish and was not happy to develop the allergy). It meant that anything with seafood was labelled carefully for company potlucks. Plenty of people did eat products that contained peanuts and/or shellfish at restaurants nearby during their lunch hour.
The employee should be able to advise your HR department in greater detail about how her allergy needs to be accommodated, and then employees can be informed about the reasonable accommodation that is being offered.