Act I is usually marked by the "hero's" commitment to his "journey." Whether you focus on Georgiana or on Aylmer as the story's "hero," we can be pretty sure Act I takes us through the couple's decision to remove the birthmark.
Drama in the lab. Aylmer shows Georgiana his scientific stuff; she thinks it's cute until she finds him pale-faced and sweaty in front of his furnace.
The couple reconcile and decide to move forward with the procedure. Georgiana drinks the elixir, but quite unfortunately dies right after.