Welcome to the SR family!
I'm sorry about your cousin's condition.
We are not allowed to give out medical advise on this forum. I would not be able to tell you how long she has, infact, a doctor trained in addiction would only be able to give you an estimated time frame.
If she gets help today, the withdrawals from alcohol may kill her.
Have you considered attending Al-anon meetings for face-to-face support in your community? Alanon meetings are based on the same 12 steps as Alcholics Anonymous but tailored to for the family and friends of the alcoholic. You will find information and support at the meetings,, as well as here at SR.