She totally could have. But other means of suicide give family and bystanders a chance to intervene. Pills and alcohol can be pumped out of the stomach. You can be pulled down from the edge of a bridge. You can rescue yourself from a hanging if you find you have last minute regrets.
A gun is brutally efficient at killing you; Load and pull the trigger. If the gun is lying around loaded, all you have to do is pick it up and pull. A gentle flick of the finger and it's over.
Even if we were to agree with such a right, you would have a duty about how you do it to reduce trauma to others and society has a duty to make sure it is a rational choice. Also, even in a world where adults would have that right, but I doubt those under 18 would without special circumstances such as terminal illness.
A gun is brutally efficient at killing you; Load and pull the trigger. If the gun is lying around loaded, all you have to do is pick it up and pull. A gentle flick of the finger and it's over.