A. No they should not be euthanized. A one year old isn't the same thing as a puppy with say a heart defect. The choice is with the parents, not by some entity or the likes of yourself who thinks they know better than the parents of what is best for THEIR child.
B. Until you have child of your own you won't know the experience of being a parent. It takes a lot of courage to take grandpaw off the vent. Now what kind of courage would it take to take your one year old and let him/her die?
Now before you get your panties in a bunch, understand I am in the medical field and have done plenty of extreme measures to keep people alive. Mostly because the family doesn't want to face the reality of the situation or the family has no advance directive by grandma of what her wishes are. So I understand the quality of life issue.
And BTW, you don't know what kind of life she is going to have. At least her parents will be there so she can enjoy the last 2 years of her life being loved by her parents.