Kate Stone is "progressing daily" in hospital and has been moved from the high dependency unit to a regular ward.
The 44-year-old was injured by the animal near Fort William in the Highlands in the early hours of Monday December 30.
She was placed in an induced coma on New Year's Eve following an operation at Glasgow's Southern General Hospital to repair damage to her windpipe, and was taken off sedation the following week.
A statement released by a colleague at Dr Stone's print firm Novalia said: "Kate still remains in Southern General Hospital and is progressing daily with her recovery.
"She has been moved out of high dependency and is now in a regular ward where she is continuing to receive care from doctors and nurses.
"Kate is now in a realistic state of mind since coming out of her medically induced coma and is able to speak to her family and nurses as well as walk short distances.
"She will continue with her physiotherapy and hopefully continue to improve with each passing day."
Dr Stone, from Cambridge, was on a short break with friends when the stag ran towards her and gored her while she was standing outside a private residence in Lochailort.
She was taken to Belford Hospital in Fort William before being transferred by air to Southern General.