There is a site/app called, “Find Me Gluten Free”. I checked it, but no luck. Best to bring your own. I would just bring or buy some other treats. Save your gluten-free Beignets for when you are at home and they come out of the fryer. Hot. Yum.
Personally, I would skip the gluten-free donuts. I could not find any dedicated gluten-free bakeries in New Orleans. I would worry about cross contamination where flour in the air is possible.
You should be able to indulge in coffee. 😊